Applications Of Derivatives Question 388
Question: The function $ f(x)=x(x+3){e^{-(1/2)x}} $ satisfies all the conditions of Rolle’s theorem in [-3, 0]. The value of c is
Options:
A) 0
B) -1
C) - 2
D) - 3
Show Answer
Answer:
Correct Answer: C
Solution:
To determine ‘c’ in Rolle’s theorem, $ f’(c)=0 $ .
Here $ f’(x)=(x^{2}+3x){e^{-(1/2)x}}.( -\frac{1}{2} )+(2x+3){e^{-(1/2)x}} $
$ ={e^{-(1/2)x}}{ -\frac{1}{2}(x^{2}+3x)+2x+3 } $
$ =-\frac{1}{2}{e^{-(x/2)}}{x^{2}-x-6} $
$ \therefore f’(c)=0\Rightarrow c^{2}-c-6=0\Rightarrow c=3,,-2, $ But $ c=3\notin [-3,,0]. $
BETA
