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Derivative Rules for Piecewise and Absolute Value Functions
Grade Level
Calculus I
CAL1.69 Derivative Rules for Piecewise and Absolute Value Functions
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Use derivative rules to choose the correct statement for f(x) = {|x
2
- 1| for x < 2; 3x - 5 for x >= 2}.
A
f'(x)=2x for x < -1; f'(x)=-2x for -1 < x < 1; f'(x)=2x for 1 < x < 2; f'(x)=3 for x > 2; f is differentiable at every point in its domain
B
f'(x)=2x for x < -1; f'(x)=-2x for -1 < x < 1; f'(x)=2x for 1 < x < 2; f'(x)=3 for x > 2; not differentiable at x=-1, x=1, and x=2
C
f'(x)=3 for x < -1; f'(x)=2x for -1 < x < 1; f'(x)=-2x for 1 < x < 2; f'(x)=2x for x > 2; not differentiable at x=-1, x=1, and x=2
D
f'(x)=2x for x < -1; f'(x)=-2x for -1 < x < 1; f'(x)=2x for 1 < x < 2; f'(x)=3 for x > 2; not differentiable at x=-1 and x=1
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