Question

Is the graph of y = sin(x
5
) increasing or decreasing when
x = 12? (enter increasing, decreasing, or neither).
Is it concave up or concave down? (enter up, down,
or neither).

Answer 1

$f(x)=\sin x^5;$

$f'=5x^4\cos x^5; f(12)=5*12^4\cos(12^5)=5*12^4\frac{\sqrt{5}-1}{4}>0$

Hence the graph is increasing.

$f''=20x^3\cos x^5-25x^8\sin x^5; f''(12)<0$

Hence the graph concaves down.