ƒ(x) = (1/4)x^4 - 2x^2

Question

ƒ(x) = (1/4)x⁴ - 2x²

(a) Find the intervals on which ƒ is increasing or decreasing.

(b) Find the local maximum and minimum values of ƒ.

(c) Find the intervals of concavity and the inflection points.

Answer 1

a) find f' = x³-4x, set f'= 0 and find x_c=0,+2,-2 Note that f'>0 for -2<x<0 and 2<x, f'<0 for -2>x and 0>x>2

b) sub x_c into f to find f(0)=0, f(2)=4, f(-2)=4

c) find f'' = 3x²-4 to find inflection points at ±-2/√3 note that f''>- for -∞>x>-2/√3 for CCU, f''<0 -2/√3>x>2/√3 for CCD

Answer 2

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