Help Calculus

[zealous light]

Help me with calculus

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[neon mango]

Critical points are when f’(x)=0.

[zealous light]

I got that, so I know the critical points are -2, 1, and 4

And a critical point is a relative maximum when it goes from positive to negative

With that, I got that only -2 was a relative maximum, but a friend got all three as relative maximums

So I’m not sure if I’m doing it right or if he’s wrong

[neon mango]

Take the second derivative and plug in the x-value (if it is negative, it is a minimum, if it is positive, it is a maximum).

[zealous light]

I’m not too sure how I would get the second derivative here, I’m only given a graph of the first derivative and no equation

[digital bough]

Your friend is definitely wrong.

[digital bough]

Because this is definitely correct, because recall what the first derivative is. It's the graph of the slope of the tangent line. Now visualize an absolute maximum and focus on what the slope is doing as the point of tangency moves across it.

[neon mango]

Notice the behavior of f’ in a neighborhood of x=root (in other words, is the derivative going from positive to negative)?

[past harbor]

Aka the first derivative test

[heavy lantern]

@zealous light

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