DifferentiationHard

Question

If f(x) = | (x - 4) (x - 5) |, then f¢(x) is equal to

Options

A.-2x + 9, for all x ∈ R
B.2x - 9 if x > 5
C.-2x + 9 if 4 < x < 5
D.not defined for x = 4, 5

Solution

f(x) = |(x - 4) (x - 5)|
f′(x) = 2x - 9, x > 5                        
f′(x) = -2x + 9, 4 < x < 5
Not defined at x = 4, 5 by graph

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