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March 28, 2015

March 28, 2015

Posted by **Cesar** on Wednesday, February 23, 2011 at 8:35pm.

f(x) = { -7x^2 + 7x for x<=0

{ 3x^2 + 7x for x>0

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

lim x-> 0− = _____

and the right-hand limit

lim x->0+ ______

We conclude that f'(0)= _____

Write DNE if the derivative does not exist.

Ok... I know that the answer for f'(0) is 7... I thought that the answers for the previous 2 were 0 because I was left with -7x for the left one and 3x for the right one... what am I doing wrong?

- Calculus -
**MathMate**, Wednesday, February 23, 2011 at 9:05pmFor x-> 0

^{-},

f'(x) = d(-7x^2 + 7x)/dx = -14x+7 = 7

For x-> 0^{+},

f'(x) = d(3x^2 + 7x)/dx = 6x + 7 = 7

Since f'(0^{-}) = f'(0^{+}) = 7,

f'(0) exists, and equal to 7.

- Calculus -
**Cesar**, Wednesday, February 23, 2011 at 9:08pmI already tried 7 for the first two... but the web ways that the answer is incorrect...

- Calculus -
**Cesar**, Wednesday, February 23, 2011 at 9:29pmI have no idea why that's not the answer.....

- Calculus -
**MathMate**, Wednesday, February 23, 2011 at 11:40pmYou may want to check if there is no typo somewhere.

Other than that, I cannot think of anything else.

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