JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)=\int_0^{x^2} \frac{\mathrm{t}^2-8 \mathrm{t}+15}{\mathrm{e}^{\mathrm{t}}} \mathrm{dt}, x \in \mathbf{R}\). Then the numbers of local maximum and local minimum points of \(f\), respectively, are :
- A 2 and 3
- B 2 and 2
- C 3 and 2
- D 1 and 3
Answer & Solution
Correct Answer
(A) 2 and 3
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=\int_0^{x^2} \frac{t^2-8 t+15}{e^t} d t, x \in R \\ & f^{\prime}(x)=\frac{x^4-8 x^2+15}{e^{x^2}}(2 x)=0 \\ & \Rightarrow \quad \frac{2 \times\left(x^2-5\right)\left(x^2-3\right)}{e^{x^2}}=0 \\ & \Rightarrow…
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