Q. 8
Verify Rolle’s theorem for each of the following functions:
Answer :
Condition (1):
Since, f(x)= x3+3x2-24x-80 is a polynomial and we know every polynomial function is continuous for all xϵR.
⇒ f(x)= x3+3x2-24x-80 is continuous on [-4,5].
Condition (2):
Here, f’(x)= 3x2+6x-24 which exist in [-4,5].
So, f(x)= x3+3x2-24x-80 is differentiable on (-4,5).
Condition (3):
Here, f(-4)= (-4)3+3(-4)2-24(-4)-80=0
And f(5)= (5)3+3(5)2-24(5)-80=0
i.e. f(-4)=f(5)
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one cϵ(-4,5) such that f’(c)=0
i.e. 3c2+6c-24=0
i.e. c=-4 or c=2
Value of c=2 ϵ(-4,5)
Thus, Rolle’s theorem is satisfied.
Rate this question :
Practise Questions - Application of Derivatives45 mins
How to find Maxima & Minima?43 mins
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)52 mins
Tangents & Normals (Concept Builder Class)55 mins
Few Applications of Gauss's law54 mins
Application of Biotechnology | Concepts - 0256 mins
Applications of Ampere's Circuital Law44 mins
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
