Let f(x) be a polynomial of degree 3 such that f(-1)=10,f(1)=-6,f(x) has a critical point at x=-1 and f'(x) has a critical point at x=1 . Then f(x) has a local minima at x=
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answer is 3.
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Detailed Solution
f'(-1)=0&f(-1)=10⇒ Local maxima at x=-1 Let f''(x)=k(x-1)∵f''(1)=0⇒f'(x)=k2x2-2x+cf'(-1)=0⇒c=-3k2f'(x)=k2(x+1)(x-3)⇒ Local minima at x=3