The sign of the derivative of a twice-differentiable function is described below

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The sign of the derivative f′(x)f'(x) of a twice-differentiable function ff is described below. • (0,2):  f′(x)>0(0,2):\;f'(x)>0 • x=2:  f′(x)=0x=2:\;f'(x)=0 • (2,4):  f′(x)<0(2,4):\;f'(x)<0 • x=4:  f′(x)=0x=4:\;f'(x)=0 • (4,6):  f′(x)<0(4,6):\;f'(x)<0 • x=6:  f′(x)=0x=6:\;f'(x)=0 • (6,8):  f′(x)>0(6,8):\;f'(x)>0 Determine the xx-value at which ff attains a local maximum on 0<x<80<x<8.

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