Calculus

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Sorry for posting another quesiton..;

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 -

    For 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 -

    I already tried 7 for the first two... but the web ways that the answer is incorrect...

  • Calculus -

    I have no idea why that's not the answer.....

  • Calculus -

    You may want to check if there is no typo somewhere.
    Other than that, I cannot think of anything else.

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