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# According to the alternate form of the definition of the derivative, to compute f'(0), we need to compute the left-hand limit

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Let

$$f(x)= \begin{cases} -4x^{2}+4x & \text{for } x < 0, \\ 7x^{2}-5 & \text{for } x \geqslant 0. \end{cases}$$

According to the alternate form of the definition of the derivative, to compute $$f'(0)$$, we need to compute the left-hand limit

$$\lim \limits _ {x \to 0^-}$$ ?, which is ?,

and the right-hand limit

$$\lim \limits _ {x \to 0^+}$$ ?, which is ?.

Mar 9, 2022

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Like this:

Mar 9, 2022

### 3+0 Answers

#1
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The left-hand limit is 0.

The right-hand limit is -5.

Mar 9, 2022
#2
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This answer is incorrect on my side. I think this problem should be looked over again to find the solution.

GAMEMASTERX40  Mar 9, 2022
#3
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Best Answer

Like this:

Alan Mar 9, 2022