Question

Find the maximum height of the curve
y = 4 sinx - 3 cos x abive the x axis

Answer 1

To find x at which y becomes maximum, find the first derivative by x and equate it to 0:

$$y'=4\cos x+3\sin x =0,\\\space\\ \tan x=\frac 43,\\\space\\ x=53°.\\\space\\ y_\text{max}=4\sin53°-3\cos53°=1.39.$$