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
5 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
please help .........
 
 
Hi student Let sinx= t 2t 2 +3t – 2 = 2t 2 +4t -t -2 = 2t(t+2) -1(t+2)= (2t -1)(t+2) Now given (2t-1)(t+2)>0 => t>1/2 or t<-2 => sinx> ½ or sinx <-2 (not...
  img
Harsh Patodia one month ago
 
in equation 1 ...can i write 2pi/3 (pi/2+pi/6).......instead of 5pi/6 ….….….…....
 
milind one month ago
help ...please explain fully
 
 
oh sorry i couldnot chat yesterday. i logged off. i will explain. you can do this question in many ways easiest method to save time is differentiate both sides of the equation. keeping...
 
esha singh 5 months ago
 
its a bit lengthy (limits method) i find this method more appealing.
 
esha singh 5 months ago
 
is the answer none of these ?
 
esha singh 5 months ago
please explain fully …...if it is 0/0 form than tell why ….…..please
 
 
Ans: If the given function in the limit is of zero by zero form, then we can apply L’Hospital rule which is explain below f(a) = 0 g(a) = 0 Similarly follow for higher derivative. We...
  img
Jitender Singh 5 months ago
 
jitendra sir my question is not ..to explain l hospital rule ….….my question is that the image that i attach have 0/0 form …. how it have 0/0 form.....................jo maine question...
 
milind 4 months ago
(*) If A,B are acute angles, tan A = n/(n+1), tan B = 1/(2n+1), then A+B =
 
 
Hi, Follow the steps to reach to the answer : Apply the TAN (A+B) formula in terms of TAN (A) and TAN (B) and substitute the values. Upon simplification ull get TAN (A+B) = 1, i.e. A+B =...
  img
Yash Baheti 3 months ago
A particle begins at the origin and moves successively, 1 unit to the right, 1/2 unit up, 1/4 unit to the left, 1/8 unit down, 1/16 unit to the right, 1/32 unit up etc.The length of each...
 
 
ans: total displacement in X direction : step-1 : 1 unit right (+ve X direction) step-3 : 1/2 2 unit left (-ve X deirction) step-5: 1/2 4 unit right ( +ve X direction) step-7 : 1/2 6 unit (...
  img
Ajay Verma 10 months ago
 
x coordinate = 1-(1/4)+(1/16)-(1/64)....... y coordinate = (1/2) -(1/8) + (1/32) ......... converge the above two series to get the X and Y as the result of converging coordinate Thanks...
  img
Saurabh Singh 10 months ago
how many 7 digit numbers can be formed using digits 1,2,0,2,4,2,4
 
 
with repetion of digits _|_|_|_|_|_|_| since you have seven blanks to fill therefore in the first blank we have 6 chocies to fill as we cant use 0 or the number will be 6 digits . so we have...
 
Ashwin 4 months ago
View all Questions »