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Chapter 1: Q. 1 (page 137)

Calculate the derivative of $f (x) = x^{2}$ at $c = 0$ .

Short Answer

Expert verified

The derivative is $0$ .

Step by step solution

Step 1. Given Information.

We are given a function,

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

Step 2. Finding the derivative.

The derivative is given by,

$f^{'} (c) = \lim_{h \to 0} \frac{f (c + h) - f (c)}{h} f^{'} (0) = \lim_{h \to 0} \frac{(0 + h)^{2} - (0)^{2}}{h} = \lim_{h \to 0} \frac{h^{2}}{h} = \lim_{h \to 0} h = \lim_{h \to 0} 0 = 0$

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements in Exercises $47 - 60 .$

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Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

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Calculate each of the limits:

$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

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Calculate the derivative of f(x)=x2 at c=0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the derivative.

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Most popular questions from this chapter

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Calculate the derivative of $f (x) = x^{2}$ at $c = 0$ .