If f(x) is a polynomial function which satisfy the relation (f(x))2 f"(x)=(f"(x))3 f'(x), f'(0)=f'(1)=f'(-1)=0,f(0)=4, f(±1)=3, then f"(i) (where i=√7) is equal to


Please show complete solution

2 years ago

Share

Answers : (1)

                                        
Ans:
f'(0) = f'(-1) = f'(1) = 0
\Rightarrow f'(x) = ax(x-1)(x+1), a = constant
\int df(x) = \int ax(x-1)(x+1)dx
f(x) = a(\frac{x^{4}}{4}-\frac{x^{2}}{2}) + c, c = constant
f(0) = a(\frac{0^{4}}{4}-\frac{0^{2}}{2}) + c = 4
\Rightarrow c = 4
f(\pm 1) = a(\frac{(\pm 1)^{4}}{4}-\frac{(\pm 1)^{2}}{2}) + 4 = 3
\frac{-a}{4} = -1
a = 4
f(x) = x^{4}-2x^{2}+4
f'(x) = 4x^{3}-4x
f''(x) = 12x^{2}-4
f''(\sqrt{7}) = 12(\sqrt{7})^{2}-4 = 80
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
2 months ago

Post Your Answer

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
Find the period of the valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6)
 
 
Hello Student, f(x)+f(x+4)=f(x+2)+f(x+6) =>f(x+2)+f(x+6)=f(x+4)+f(x+8) adding both we get f(x)=f(x+8) Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar one month ago
what is meant by ccontunity of functions
 
 
Ans: Continuity of a function at a given point means that it should exist at the given point & left hand limit & right hand limit should exist & equal to each other &...
  img
Jitender Singh 2 months ago
Please prove …..and also give explanation sir please
 
 
Ans: Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty
  img
Jitender Singh one month ago
 
Sir but what is answer
 
milind one month ago
A person goes to office either by car, scooter, bus or train probability of which being 1/7 , 3/7 , 2/7 and 1/7 respectively. Probability that he reaches office late, if he takes car,...
 
 
Hello Student, P(C)=1/7 P(S)=3/7 P(B)=2/7 P(T)=1/7 I be the event of him reaching in time. P(I/C)=7/9 P(I/S)=8/9 P(I/B)=5/9 P(I/T)=8/9...
  img
Arun Kumar one month ago
area of triangle
 
 
area of triangle=( Base * height ) / 2
 
Saloni gordhan Rakholiya 2 days ago
 
area of triangle=( Base * height ) / 2
 
Saloni gordhan Rakholiya 2 days ago
Is the topic Vectors hard?
 
 
very easy.....make a firm grip on it becauz it is the basic thing of phy PLZ APPROVE MY ANS
 
larisha sharma one year ago
 
if u wont command it then u will face a lot of problems in many chapters...
 
Saurabh Anand one year ago
 
it is not very tough but you can take it as average.
 
Madhukar Thalore one year ago
View all Questions »