Question

17.
Given that y=sin 3x +4/3 cos3x. What is the
maximum rate of change in y with respect to x ?​

Answer 1

Answer:

dy/dx=3cos3x-4sin3x

Step-by-step explanation:

by putting the formula

d/dx(sinx)=cosx

d/dx(cosx)=-sinx

I hope it will help you.

Answer 2

Answer:

As in the question it is given to find the maximum change in y with respect  to x that means the double differentiation of the function y must be < 0.

First we have to find the differentiation of the function y which is:-

dy/dx = d/dx(sin3x) + d/dx(4/3cos3x).

dy/dx = 3cos3x + 4/3{-3sin3x}.

dy/dx = 3cos3x  -  4sin3x.

Now to find the maximum value we need to find x which we can find by taking dy/dx = 0

3cos3x = 4sin3x.

tanx= 3/4.

So, x= tan^-1(0.75) = 36.