Question

verify it .......theorem of rolles ​

Answer 1

Answer:

hlo harish ...plz refer pic above.....✌

Answer 2

Answer :

Rolle's theorem is applicable,if

1) function is continuous in given closed interval.

2) function is differentiable in given closed interval.

3) f(a)=f(b)

we need not to check these conditions, here since function is Rolle's applicable.

$f(x) = {e}^{x} sinx \\ f'(x) = {e}^{x}sinx + {e}^{x} cosx \\ \\ f'(c) = {e}^{c}sin \: c + {e}^{c} cosc = 0 \\ {e}^{c} (sin \: c + cos \: c) = 0 \\ \\ sin \: c = - cos \: c \\ \frac{sin \: c}{cos \: c} = - 1 \\ \\ tan \: c = - 1 \\ \\ tan \: c = tan \: (\pi - \frac{\pi}{4} ) = tan \: ( \frac{3\pi}{4} ) \\ \\ c = \frac{3\pi}{4}$

So, the answer is option a, c= 3π/4.