Question

Suppose that g(x) is a polynomial function and f(x) = (x 􀀀 a)^2(x 􀀀 b)^2g(x); a ; b real numbers.
(a) Show that f'(x) has at least one zero in the interval (a; b).
(b) If g(x) is a constant, find the zero(s) of f'(x) in (a; b).

Answer 1

Latex doesn't show what the function is.

Answer 2

the function is
f(x)= (x-a)^2.(x-b)^2.g(X)