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The interval in which f(x)=int(0)^(x){(t...

The interval in which `f(x)=int_(0)^(x){(t+1)(e^(t)-1)(t-2)(t-4)}` dt increases and decreases

A

increases on `(-oo,-4)cup(-10)cup(2,oo)` and decreases on `(-4,-1)cup(0,2)`

B

increases on `(-oo,-4)cup(-12)` and decreases on `(-4,-1)cup(2,oo)`

C

increases on `(-oo,-4)cup(2,oo)` and decreases on `(-4,2)`

D

increases on `(-4,-1)cup(0,2)` and decreases on `(-oo,-4)cup(-10)cup(2,oo)`

Text Solution

AI Generated Solution

The correct Answer is:
To determine the intervals in which the function \( f(x) = \int_{0}^{x} (t+1)(e^{t}-1)(t-2)(t-4) \, dt \) is increasing or decreasing, we need to follow these steps: ### Step 1: Find the derivative of \( f(x) \) By the Fundamental Theorem of Calculus, the derivative of \( f(x) \) is given by: \[ f'(x) = (x+1)(e^{x}-1)(x-2)(x-4) \]
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