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Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If lim x→0 ((f(x)/x²) + 1) = 3 then f(-1) is equal to -
- 1/2
- 3/2
- 5/2
- 9/2
Correct answer: 9/2
Solution
From lim(f/x^2+1)=3 we get f(0)=0, f'(0)=0 and the x^2 coefficient = 2. Extrema at x=1,2 fix the quartic as f(x)=(1/2)x^4-2x^3+2x^2. Then f(-1)=1/2+2+2=9/2.
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