A calculus problem by vishnu c

Calculus Level 5

Let f(x)=(xa)(xb)3(xc)5(xd)7f(x) = (x-a)(x-b)^3 (x-c)^5 (x-d)^7 , where a,b,c,da,b,c,d real numbers with a<b<c<da<b<c<d.

Consider the derivative of f(x)f(x), f(x)f'(x). Find the number of distinct real roots of f(x)=0f'(x) = 0 .

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