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Question

If fx=x2-10x+25, then the derivative of f (x) in the interval [0, 7] is
(a) 1
(b) −1
(c) 0
(d) none of these

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Solution

(d) none of these

We have, fx=x2-10x+25=x-52=x-5 =x-5 for x>5 -x-5 for x<5LHD=limx5- fx-fax-a =limx5-x2-10x+25-52-105+25x-5 =limx5-x-5x-5 =limx5--x-5x-5 =-1RHD=limx5+ fx-fax-a =limx5+x2-10x+25-52-105+25x-5 =limx5+x-5x-5 =limx5+x-5x-5 =1Here, LHDRHDThus, the functionis not differentiable at x=5

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