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Find the points. At which f(x)=x |x-x^2|is not differentiable in [-2 to 2]

Find the points. At which f(x)=x |x-x^2|is not differentiable in [-2 to 2]

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
The points of interest are just the 0 and 1

f(0) = f(1) = 0
f'(x) = 2x-3x^2, \forall x \in (0,1)
f'(x) = -2x+3x^2, \forall x \in (-\infty,0)\cup(1,\infty)
we can see that for x = 0 both differentials are equal and hence its a differential point but for x=1 they are not equal and hence the only not-differentiable point in f(x) is x=1

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