The value of `c` in Rolles theorem for the function `f(x)=(x(x+1))/(e^x)` defined on `[-1,\ 0]` is `0. 5` (b) `(1+sqrt(5))/2` (c) `(1-sqrt(5))/2` (d) `-0. 5`

Answer

value of `C` is `frac{1-sqrt{5}}{2}`.


Option (C)

Explanation

Given:
$$ f(x)=\frac{x(x+1)}{e^{x}} $$
Differentiating the given function with respect to `x`, we get
$$ f^{\prime}(x)=\frac{e^{x}(2 x+1)-x(x+1) e^{x}}{\left(e^{x}\right)^{2}} $$
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