MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12
        
if f'(x) is continuous in [a,b] and differentiable in (a,b). Show that there exist a c in (a,b) such that f(b)=f(a)+(b-a)f'(a)+(b-a)^2f''(c)/2
5 months ago

Answers : (1)

Aditya Gupta
1690 Points
							
consider g(x)= f(b) – f(x) – f’(x)(b – x). obviously g’(x)= (x – b)f”(x)
now define h(x) = g(x) – [(b – x)/(b – a)]^2*g(a)
note that h(a)= h(b)= 0
so apply rolles theorem on h.
h’(c)=0 for some c in (a, b)
or g’(c)= 2(c – b)g(a)/(b – a)^2
or (c – b)f”(c)= 2(c – b)g(a)/(b – a)^2
or (b – a)^2f”(c)/2= g(a)
or (b – a)^2f”(c)/2=  f(b) – f(a) – f’(a)(b – a)
or f(b)=f(a)+(b-a)f'(a)+(b-a)^2f''(c)/2
kindly approve :)
5 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details