AP EAMCET · Maths · Application of Derivatives
If Rolle's theorem is applicable for the function \(f(x)=x(x+3) e^{-\frac{x}{2}}\) on \([-3,0]\). then the value of \(c\) is
- A 3
- B 3 and -2
- C -2
- D -1
Answer & Solution
Correct Answer
(C) -2
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x(x+3) e^{-\frac{x}{2}},[-3,0]\) \(\because f^{\prime}(x)=\frac{d}{d x}\left(\left(x^2+3 x\right) e^{\frac{-x}{2}}\right)=\frac{1}{2}\left(-x^2+x+6\right) e^{\frac{-x}{2}}\) Since, \(f(x)\) is satisfy Rolle's theorem so, \(c \in[-3,0]\) such that…
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