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Draw the graph of y = cos^(2)x....

Draw the graph of `y = cos^(2)x.`

Text Solution

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We have `y=f(x)=cos^(-1)(x^(2))`
Here f(x) is defined if `0 le x^(2) le 1" or "-1 le x le 1`
`Now" "f(-1)=f(-1)=cos^(-1)1=0`
`f(0)=cos^(-1)0=pi//2`
`f'(x) = (-2x)/(sqrt(1-x^(4)))`
`f'(x) =0thereforex=0`
For `xlt0,f'(x)gt0," where f(x) jincreases"`.
For `xgt0, f'(x) lt0, " where f(x) decreases".`
Also f(x) is differentiable in (-1, 1).
`f'(x)=(-2(1+x^(4)))/((1+x^(4))^(3//2))lt0`
Hence the graph of the function in the following figure.
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