# A calculus problem by vishnu c

Calculus Level 5

Let $$f(x) = (x-a)(x-b)^3 (x-c)^5 (x-d)^7$$, where $$a,b,c,d$$ real numbers with $$a<b<c<d$$.

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

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