Question

The ratio of the greatest value of 2-cos x+sin^2x to its lowest value is

Answer 1

Answer:

The answer is  13/4.

Step-by-step explanation:

Here, f(x)=2−cosx+sin^2x

f'(x)=sinx+2sinxcosx=sinx(1+2cosx)

Now, for maximum and minimum value,

f'(x)=0

Since,

   sinx(1+2cosx)=0

⇒ sinx=0 and 1+2 cosx=0

⇒ x=0 and cosx=−1/2

⇒ x=0andx=2π/3

Now, f(0)=2−1+0=1

f(2π/3)=2−(−1/2)+(3/4)=13/4

The minimum value of f(x) is 1 and maximum value of f(x) is 13/4.

Thus the ratio of greatest value to ratio of lowest value is 13/4.