Absolute Value Questions and Answers

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Solve the absolute value inequality. |1 - 4k| is greater than or equal to -11

If f(x)= 4\left | x - 7 \right |, what is f(x + 1)?

Solve 2x + (x - y)^3 when x = 9 and y = 7.

Extrema. There are two types of extrema of a given function, say f. One is relative extrema, which is a "local" property of f. The other is absolute extrema which is a "global" (or overall) property o

Solve the absolute value equation: 2*absolute of (3x - 5) - 8 = 8.

Order the following numbers from least to greatest. sqrt(7), -2.3, sqrt(3), 5.1, -1/3.

Consider the function f(x)= \frac{3x^4 - 5x + 3}{x^4 + 1}. Find: a. Domain b. Vertical, horizontal,or slant asymptotes c. x and y-intercepts d. Symmetry (respect to x- axis, y-axis or orgin)

Solve the absolute value equation. |3n + 5| = 7

A car rents for $40 per day plus 21 cents per mile. You are on a daily budget of $82. What mileage will allow you to stay within your budget?

f(x)=|x+5|; f(a)=9 find smallest value and largest value.

Give an example of an inequality represented by a graph. Explain how to derive inequality equation from a graph.

Determine all the absolute extreme values for the function f(x,y) = sin(x)*sin(y)*sin(x+y)

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 \cos t + 4 \sin 2t, parentheses 0, \frac{\pi}{2} parentheses

You are given the function f(x,y)=2x^2 +3y^2-4x-5. You have used the Second Derivative test to classify the critical point(s), which is a local minimum at __(1,0)__ a) Find the extreme values of f(x,

Find the absolute maximum and minimum values of the function. \\ f(x, y) = 2x^2 + 3y^2 - 4r - 5 \\ on the region x^2 + y^2 \leq 16.

Let f(x, y) = 2 + sqrt(3(x - 1)^2 + 4(y + 1)^2). A) Find the critical points of f. B) Find the local and absolute minimum values of f. Where do these values occur?

let f(x)= 2 - |2x-1| . Show that there is no value of c such that f(3)- f(0) = f'(c)(3-0) . Does this contradict the mean value theorem?

Find f'(3) and f'(5), if f(x) = |x - 4|.

Let M=1000. Which of the conditions is equivalent to { f(x)= \frac{1}{((4x-12)^2)} M? } a. absolute value of (x+3) { \geq .00158 } b. absolute value of (x+3) { \geq .0553 } c. absolute value o

Find the absolute maximum and minimum of the function y=2\cos(t)+\sin(2t) on the interval of parentheses 0, \frac{\pi}{2} parentheses.

b) Find an x-value in this interval where f(x) achieves its average value. c) Draw a picture illustrating your results.

Use the graph to locate absolute extrema (if they exist) of the function on the given interval. f(x) = \frac{1}{x^2 -1} on (a) (0, 1) \cup (1, \infty), (b) (-1, 1), (c) (0, 1), (d) [- \frac{1}{2}

Let f(x) = 3x^5 - 15x^4 - 50x^3 + 210x^2 - 225x + 1. (a) Find all the critical numbers of f. (b) Use the Extreme Value Theorem to explain why f is guaranteed to have an absolute maximum value and an

By using Lagrange multipliers. Find the maximum and minimum of f(x,y) = x^2- y^2 + 2x on the disk x^2 + y^2 less than or equal to 4. 1. Find the critical point in the disk and evaluate. 2. Using Lag

if | \sin x + \cos x| = | \sin x| + | \cos x| then x belongs to which quadrant?

The solution set of the equation |(2x-1)| + |(4-2x)| = 3 is,

If { \frac{x}{( 1+x )} } then what is x ?

Let f(x)=-x^2+3x on the interval parentheses 1,3 parentheses. Find the absolute maximum and absolute minimum of f(x) on this interval.

if the derivative of f is f'(x) = ln(x^2 + 1) - 2, at which of the following values of x does f have an absolute value? a) 2.53 b) 0 c) 2.72 d) 4.44 e) 1.72

{ lim_{x \to 0.5^-} \frac{(2x-1)}{|(2x^3-x^2)|} }

Find the exact location of all the relative and absolute extrema of the function. f(x) = 4x^2 - 16x + 4 with domain [0, 3] . Find the exact location of all the relative and absolute extrema of the fu

Use the method of Lagrange multipliers to find the absolute maximum and minimum values of f(x, y) = x^2 + y^2 - x - y + 2 on the unit disc, namely, D = \{(x, y)| x^2 + y^2 less than or equal to 1\}.

Find the points at which __y=f(x)=3x-ln(4x)__ has a global maximum, __a__ global minimum, and __a__ local, non-global maximum on the interval .1≤x≤2. \ 5. \ 1≤x≤2. \ 5. Round your answers

The side of a square is measured to be 12 inches with a possible error of 0.02 inch in that measurement. If x is the exact length of the side of the square, express this difference as an absolute val

If we find the critical numbers of the function g(t) = |5 t - 7|, we get g'(t) = 5 (verify this result) so would there be no critical numbers? Give reason.

Write an absoulate inequality, with 53% of the people believing they will win, and there was a 0.5% error in the prediction.

For the function f(x)=x^3e^x, determine intervals of increase and decrease and the absolute minimum value of f(x). Also, find the absolute minimum value.

Solve the inequality. { x^3 + 9x^2 -108 \leq 0 }. Then write in interval noation.

Consider the function f(x) = x - 8 |x| - 8 . (a) Find the discontinuities of f(x). x =[{Blank}] (smaller) x = [{Blank}] (larger) (b) What graphical feature does each discontinuity correspond to?

Determine the absolute minimum and absolute maximum values of f on the given interval. f(t) = 4cos t + 2sin 2t, [0, pi/2].

Find the absolute maximum and the absolute minimum values of f(x) = x - 7cos(x) on the interval [-theta ,theta ].

Sketch the graph of f(x) = \left\{\begin{matrix} 1-x & 0 \leq x \lt 2 \\ 3x-6 & 2 \leq x \leq 7 \end{matrix}\right. by hand and use your sketch to find the absolute and local maximum and minimum v

Find the local and absolute extreme values of the function on the given interval a)f(x)= \sqrt{x^2+4x+8},[-3,0] b)f(x)=x-\sqrt 2\sin (x),[0\pi]

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE) f(x) = \left\{\begin{matrix} 16 - x^ 2 if -

Find the absolute maximum, M, and minimum, m, of f(x)=cosx-sin^{2x} on the domain \left [ \pi,2\pi \right ]

Find the absolute extrema of the function \(f(x)= xe^{- x^\frac{2}{18}}\) on the interval \([-2,4]\).

The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality. Write the expression for the range of diameters.\\ |x-0.1| \leq 0.01

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(x) =\left\{\begin{matrix} 64 - x^2 & if\;

f(x)=4x^{\frac{1}{3}}-x^{\frac{2}{3}} Both are raised to the power of fractions. ^ find the intervals on which f(x)f(x) f , open x close is increasing, the intervals on which f(x)f(x) f , open x close

Find the absolute extrema if they exist as well as where they occur. (Round your answer to four decimal places.) f(x) = 3x In x Select the correct answer. A. Absolute minimum of 0.0498 at x = -3: no

Find the absolute and local maximum and minimum values of f(x)=\begin{cases}1-x & 0\leq x< 2 \\ 2x-4 &-2\leq x \leq3 \end{cases}

Find the absolute extreme of the function, if they exist, over the indicated interval. Also, indicate the x-value at which each extremism occurs. If no interval is specified, use the real numbers, (-\

Graph the function by determining the key features of the curve represented by y = cube root {3 x} + 6 cos x, 0 less than or equal to x less than or equal to 2 pi. (a) Identify any local and absolute

Solve the inequality : |x| less than -11

1. Find the absolute maximum and minimum values of y = \frac{ln \ x}{x^{2}} on the interval \left [ \frac{1}{2}, 4 \right ]. 2. Show that the equation x^{3} + e^{x} = 0 has exactly one real solution.

Find (without using a calculator) the absolute extreme values of the function on the given interval. (1) f(x) = x^{4} + 4x^{3} + 15 0n [-4,1] (2) f(x) = x^{2}(3 - x) 0n [-3,4] (3) \frac{x}{x^{2}+1} on

Sketch the graph of a function on [-1, 2] that has an absolute maximum but no local maximum. Sketch the graph of a function on [-1, 2] that has a local maximum but no absolute maximum.

1. Consider f(x) = x - 20 ln(x + 3) on the interval 0 \leq x \leq 19 a) Find f'(x). b) Find the x coordinates of the global maximum and global minimum. 2. Consider the function g(t) = \frac{t +

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f f(x) = \left\{\begin{matrix} x^2 & -1 less than or equal to x less than or equal to

|r+4| - 3|s| when r = 5 and s = -1.

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