Find the critical Numbers a. h (x) = \frac{1}{3}x^3 - 4x b. g (x) = 5 x^2 - 20 x c. f (x) =...


Find the critical Numbers

a. {eq}h (x) = \frac{1}{3}x^3 - 4x {/eq}

b. {eq}g (x) = 5 x^2 - 20 x {/eq}

c. {eq}f (x) = (x^2 - 9)^{2/3} {/eq}

d. {eq}y = x^2 -6x^2 {/eq}

e. {eq}V(x) = x^4 + \frac{1}{x^2} {/eq}

f. {eq}W(x) = x^3 - 3x^2 + 3x{/eq}

Critical Numbers of a Function:

The critical numbers of a function are nothing but the the x-coordinates of the critical points which are obtained by equating

the derivative of the function to zero.Thus, if {eq}y=f(x) {/eq} be a function then the critical numbers are determined by solving {eq}f'(x)=0 {/eq} for {eq}x. {/eq}

Answer and Explanation:

a. The given function:

{eq}h (x) = \frac{1}{3}x^{3} - 4x {/eq}

The derivative of {eq}h(x) {/eq} is:

{eq}\\\\\begin{align*} h'(x) & =...

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Learn more about this topic:

Finding Critical Points in Calculus: Function & Graph

from CAHSEE Math Exam: Tutoring Solution

Chapter 8 / Lesson 9

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