Chapter 2: Q. 39 (page 184)

Use the definition of the derivative to find f' for each function f.
$f (x) = - 2 x^{2}$

Short Answer

Expert verified

$f' (x) =$ $- 4 x$

Step by step solution

Step 1. Given information.

We have been given a function:

$f (x) = - 2 x^{2}$

We have to find f' using the definition of the derivative.

Step 2. Find the derivative

Derivative of the function can be found as :

$\begin{aligned} lim_{h \to 0} \frac{f (x + h) - f (x)}{h} = lim_{h \to 0} \frac{- 2 (x + h)^{2} - (- 2 x^{2})}{h} \\ = lim_{h \to 0} \frac{- 2 (x^{2} + 2 x h + h^{2}) + 2 x^{2}}{h} \\ = lim_{h \to 0} \frac{- 4 x h - 2 h^{2}}{h} \\ = lim_{h \to 0} \frac{h (- 4 x - 2 h)}{h} \\ = lim_{h \to 0} - 4 x - 2 h \\ = - 4 x \end{aligned}$

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Use the definition of the derivative to find f' for each function f.
$f (x) = - 2 x^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative

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Use the definition of the derivative to find f' for each function f.f(x)=-2x2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

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Statistics

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Study anywhere. Anytime. Across all devices.

Use the definition of the derivative to find f' for each function f.
$f (x) = - 2 x^{2}$