Application of DerivativeHard
Question
Let f(x) = ∫ ex(x - 1)(x - 2)dx. Then f decreases in the interval
Options
A.(- ∞, -2)
B.(- 2, -1)
C.(1, 2)
D.(2, ∞)
Solution
Let f(x) = ∫ex(x - 1)(x - 2)dx.
⇒ f′(x) = ex (x -1)(x - 2)
∴ f′(x) < 0 for 1 < x < 2
⇒ f(x) is decreasing for x ∈ (1, 2)
⇒ f′(x) = ex (x -1)(x - 2)
∴ f′(x) < 0 for 1 < x < 2
⇒ f(x) is decreasing for x ∈ (1, 2)
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