Question

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?

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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