Question

verify rolles theorem on basis of this question​

Answer 1

Answer:

hlo dued please refer pic above..

Answer 2

Rolle's theorem is application of mean value theorem. in case of mean value theorem, f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a< c < b) such that 

if f'(c) = 0, it is said as Rolle's theorem,

here, f(x) = e^xsinx , x belongs to [0, π]

now, f'(x) = e^xsinx + e^xcosx

take a point c in interval [0, π] such that 0 < c < π.

then, from. Rolle's theorem, f'(c) =0

e^c [sinc + cosc] = 0

we know, e^c ≠ 0 so, [sinc + cosc] =0

sinc = -cosc

tanc = -1 = tan(π - π/4) = tan3π/4

c = 3π/4

$\rule{200}{2}$