Answer to Question #104264 in Calculus for maria

Question

s 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

$y=\sin x^5$

$y'=5x^4\cos x^5; y'(12)=5*12^4*\cos12^5>0$ therefore the graph is increasing

$y''=20x^3\cos x^5-25x^8\sin x^5; y''(12)<0$ therefre the graph concaves down