Question

The graph of y = 7cosx + 24sinx would be a sinusoid if it were plotted. What would be the first positive value of x at which there is a high point?

Answer 1

dy/dx = 0 at max or min

0= -7 sin x + 24 cos x
7 sin x = 24 cos x
tan x = 24/7
x = 73.7 degrees
is that a max or a min?
d^2y/dx^2 = -7 cos x -24 sin x
that is negative so it is a maximum