# 3) Let f(x) = 3x^4 - 8x^3 + 1. Find the critical points and classify them using the second...

## Question:

Let {eq}f(x) = 3x^4 - 8x^3 + 1{/eq}. Find the critical points and classify them using the second derivative test.

a. Find the first derivative and the critical points.

b.Find the second derivative test and classify the critical points as maximums or minimums.

## Relative Maxima and Minima:

The critical points of a function f(x) can be found by setting to zero the first derivative

{eq}f'(x) =0 {/eq}

The nature of the critical points (i.e. maximum, minimum) can be determined by

performing the Second Derivative Test.

If second derivative is positive, the extreme point is a local minimum at x.

If second derivative is negative the extreme point is a local maximum x.

If second derivative is equal to zero, the test is not conclusive.

Given the function

{eq}\displaystyle f(x) =3x^4 - 8x^3 + 1 {/eq}

its critical points are found setting the first derivative to zero

{eq}f'(x)...

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