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Let f(x) be a polynomial of degree 3 suc...

Let f(x) be a polynomial of degree 3 such that `f(-2)=5, f(2)=-3,`` f'(x)` has a critical point at `x = -2` and `f''(x)` has a critical point at x = 2. Then f(x) has a local maxima at x = a and local minimum at x = b. Then find b-a.

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Verified by Experts

The correct Answer is:
8
`f''(x) = lamda (x-2)`
`f'(x) = (lamdax^2)/2 - 2 lamda x + c" "rArr" "f'(-2) = " "rArr " "c = -6 lamda`
`:." "f'(x) = (lamda x^2)/2 - 2 lamda x - 6 lamda = lamda ( x-6)(x+2)`
` a = -2, b=6` " ":. b=a = 8`
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