Question

Given that y=sin 3x+cos3x. What is the
3
maximum rate of change in y with respect to x?
(1) 7 (2) 4 (3) 5 (4) 6​

Answer 1

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 maximum rate of change of y with respect to x , if we put x=0 then  the value of dy/dx will be 3 as cos0 is 1 and sin0 is 1.

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.

Answer 2

Answer:

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