MHB 9.1.317 AP calculus exam multiple choice derivatives of sin wave

[karush]

View attachment 9358
ok just posted an image due to macros in the overleaf doc

this of course looks like a sin or cos wave and flips back and forth by taking derivatives
looks like a period of 12 and an amplitude of 3 so...
but to start I was not able to duplicate this on desmos

altho I think by observation alone I think which choices represent the graph.

 

[skeeter]

typo in the accumulation function. should be ...

$$h(x) = \int_0^x f({\color{red}t}) \, dt$$$h'(x) = f(x) \implies h''(x) = f'(x)$$h(6) < 0$ ... why?

$h'(6) = f(6) = 0$

$h''(6) = f'(6) > 0$ ... why?