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Question

If f(x)=min(|x|25|x|,1) then f(x) is non differentiable at λ points, then λ+13 equals

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Solution


y= min (|x|2+5|x|,1)
Plot the functions
f(x)=|x|2+5|x| and g(x)=1
on the same graph paper, and then decide the minimum.
So the graph of min (|x|2+5|x|,1) is
The function will be non differentiable for all those x at which the graph takes a sharp turn. From the above graph we can see there are three sharp points (encircled).
Hence λ=3
λ+13=3+13=16

1180665_1274082_ans_58c98e462ae54c93b911f85345e3d3be.png

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