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The ratio of the greatest value of 2-cos...

The ratio of the greatest value of `2-cosx+sin^2x` to its least value is: `(A)1/4 (B) 9/4 (C) 13/4` (D) none of these

Text Solution

Verified by Experts

Here, `f(x) = 2-cosx+sin^2x`
`f'(x) = sinx +2sinxcosx = sinx(1+2cosx)`
Now, for maximum and minimum value,
`f'(x) = 0`
`:. sinx(1+2cosx) = 0`
`=> sinx = 0 and 1+2cosx = 0`
`=> x = 0 and cosx = -1/2`
`=> x = 0 and x = (2pi)/3`
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