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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)/2-2lamdax+Cimpliesf.(-2)=0impliesc=-6lamda`
`:.f.(x) = (lamdax^(2))/2-2lamdax-6lamda=lamda(x-6)(x+2)`
`a=-2 , b=6 " " :.b-a=8`
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