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We have `y=f(x)=cos^(-1)(x^(2))` <br> Here f(x) is defined if `0 le x^(2) le 1" or "-1 le x le 1` <br> `Now" "f(-1)=f(-1)=cos^(-1)1=0` <br> `f(0)=cos^(-1)0=pi//2` <br> `f'(x) = (-2x)/(sqrt(1-x^(4)))` <br> `f'(x) =0thereforex=0` <br> For `xlt0,f'(x)gt0," where f(x) jincreases"`. <br> For `xgt0, f'(x) lt0, " where f(x) decreases".` <br> Also f(x) is differentiable in (-1, 1). <br> `f'(x)=(-2(1+x^(4)))/((1+x^(4))^(3//2))lt0` <br> Hence the graph of the function in the following figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_008_S01.png" width="80%">