Q. 16
Verify Rolle’s theorem for each of the following functions:

Answer :
Condition (1):
Since, f(x)=sinx+cosx is a trigonometric function and we know every trigonometric function is continuous.
⇒ f(x)= sinx+cosx is continuous on .
Condition (2):
Here, f’(x)= cosx-sinx which exist in .
So, f(x)= sinx+cosx is differentiable on
Condition (3):
Here, f(0)=sin0+cos0=1
And
i.e.
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one such that f’(c)=0
i.e. cosc-sinc =0
i.e.
Value of
Thus, Rolle’s theorem is satisfied.
Rate this question :






















Verify the Rolle’s theorem for each of the functions
f(x) = x (x – 1)2 in [0, 1].
Mathematics - ExemplarThe value of c in Rolle’s theorem for the function f(x) = x3 – 3x in the interval
For the function the value of c for mean value theorem is
Verify the Rolle’s theorem for each of the functions
Verify the Rolle’s theorem for each of the functions
f(x) = log (x2 + 2) – log3 in [– 1, 1].
Mathematics - ExemplarDiscuss the applicability of Rolle’s theorem for the following functions on the indicated intervals :
f(x) = 3 + (x – 2)2/3 on [1, 3]
RD Sharma - Volume 1Using Rolle’s theorem, find the point on the curve y = x(x – 4), where the tangent is parallel to x-axis.
Verify the Rolle’s theorem for each of the functions
State True or False for the statements
Rolle’s theorem is applicable for the function f(x) = |x – 1| in [0, 2].
Mathematics - ExemplarDiscuss the applicability of Rolle’s theorem on the function given by