Answer :

Given:- Function f(x) = f(x) = x2 – 6x + 3


Theorem:- Let f be a differentiable real function defined on an open interval (a,b).


(i) If f’(x) > 0 for all , then f(x) is increasing on (a, b)


(ii) If f’(x) < 0 for all , then f(x) is decreasing on (a, b)


Algorithm:-


(i) Obtain the function and put it equal to f(x)


(ii) Find f’(x)


(iii) Put f’(x) > 0 and solve this inequation.


For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain it is decreasing.


Here we have,


f(x) = f(x) = x2 – 6x + 3



f’(x) = 2x – 6


f’(x) = 2(x – 3)


Here A function is said to be increasing on [a,b] if f(x) > 0


as given


x ϵ [4, 6]


4 ≤ x ≤ 6


1 ≤ (x–3) ≤ 3


(x – 3) > 0


2(x – 3) > 0


f’(x) > 0


Hence, condition for f(x) to be increasing


Thus f(x) is increasing on interval x [4, 6]


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Show that the altMathematics - Board Papers

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1