wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Find the value of c in a Rolle's theorem for the function f(x)=x33x in [3,0].

Open in App
Solution

Given function f(x)=x33x is a polynomial function.

f(x) is continuous as well as differentiable in [3,0].

Also, f(3)=(3)23(3)=33+33=0

And, f(0)=0 Thus, all the three conditions of Rolle's Theorem are satisfied.

There exist at least one real number c, such that f(c)=0

f(x)=3x23

3c23=0

c2=1

c=±1
Thus, c=1 (3,0)

Hence, value of c is 1.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon