Sketch the graph of f by hand and use your sketch to find the absolute and local

Question

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f.

f(x) = {49-x^2 if -7< = x < 0
{4x -3 if 0 < = x < = 7

Essentially I'm doubting the answers I'm getting for these problems.

I have:

Abs. Max: f(7)=25

Abs. Min:  f(0)=-3

*Loc. Max: f(7)=25 and f(0)=49

Loc. Min: f(0)=-3 and f(-2)=0

*I'm confused about the local max. Is f(0)=49 a local max, even though it's undefined? I know it's not the absolute max, but am unsure about the local. Thanks!

Explanation / Answer

If the derivative of your function is undefined somewhere in your interval, then yes, it could be a max or min. For example, the absolute value of x. The derivative of it is undefined at 0, but the graph of |x| has a minimum at x=0. If f(x) shoots up to infinity there is no max.

But is f(0) =49 , I think f(0) = -3 since second peice defines at x=0

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