wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Is Rolle's theorem applicable for the function f(x)=x36x2+11x6?

Open in App
Solution

Here, we have f(x)=x36x2+11x6,iff(x)=0
Then x36x2+11x6x=0
(x1)(x2)(x3)=0
x=1,2,3.=f(1)=0=f(2)=f(3)
Also f(x)=3x212x+11
Now Rf(x)=limh0f(x+h)f(x))h
=limh0[(x+h)3+6(x+h)2+11(x+h)6][x36x2+11x6]h
=limh0(x+h)3x36(x+h)2x2+11(x+h)x)h
=limh0(x+h)3x3h6limh0[(x+h)2x2]h+11limh0(x+h)xh
=3x212x+11.
Similarly Lf(x)=limh0f(xh)f(x)h
=limh0(xh)3x3h6limh0(xh)2x2h+11limh0(xh)xh
=3x212x+11

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