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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 36 (page 906)

Find the derivative of each function at the number indicated using a graphing utility.
$f (x) = 4 x^{4} - 3 x^{3} + 6 x - 9 a t - 2$

Short Answer

Expert verified

The derivative of the function at the number is about $- 158$ .

Step by step solution

01

Step 1. Given information.

The given function is,

$f (x) = 4 x^{4} - 3 x^{3} + 6 x - 9 a t - 2$

02

Step 2. Finding the derivative at the given number.

Now we will find the derivative of the given function at the number then we get,

$\frac{d f (x)}{d x} = \frac{d (4 x^{4} - 3 x^{3} + 6 x - 9)}{d x} = \frac{d (4 x^{4})}{d x} + \frac{d (- 3 x^{3})}{d x} + \frac{d (6 x)}{d x} + \frac{d (- 9)}{d x} = 16 x^{3} - 9 x^{2} + 6$

At $- 2$ the derivative will be,

$\frac{d f (x)}{d x} = 16 {(- 2)}^{3} - 9 {(- 2)}^{2} + 6 = 16 (- 8) - 9 (4) + 6 = - 128 - 36 + 6 = - 158$

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