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
Total number of solutions x 2 -4-[x]=0
 
 
2 Solve it graphically.
 
Drake 2 months ago
​Q. THE PARABOLAS Y 2 = 4AX AND X 2 = 4BY INTERSECT ORHTOGONALLY AT POINT P(X 1 , Y 1 ) WHERE X 1 Y 1 NOT EQUAL TO ZERO, PROVIDED- B=A 2 B=A 3 B 3 =A 2 NONE OF THESE
 
 
Ans: Hello Student, Please find answer to your question below Slope of tangent: ….........(1) Slope of tangent: …............(2) ….......(3) Point of intersection
  img
Jitender Singh 15 days ago
 
THANK YOU VERY MUCH SIR FOR ALL THE ANSWERS........
 
bharat makkar 13 days ago
Show by using LMVT f(x)=logx that 1-a/b
 
 
Hi Student, Your questions seems to incomplete. Please rewrite your complete question. Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty
  img
Jitender Singh 2 months ago
Find the real values of the parameter ‘a’ for which atleast one complex number z =x+iy satisfies both the equality |z-ai|=a+4 and the inequality |z-2| is less than 1 .
 
 
Ans: Hello Student, Please find the answer to your question below For having atleast one solution for both the equation, the first circle should intersect with 2 nd circle on the x –...
  img
Jitender Singh one month ago
 
first of all is not right as given in qus this is less than 1 not equal second thing this qus is from resonannce assignment and ans is (-21/10 ,- 5/6)
 
saurabh one month ago
x=tanA+sina y=tana-sina prove x 2- y 2= ∫4xy
 
 
LHS: x 2 – y 2 = (tanA + sinA) 2 – (tanA – sinA) 2 = 4tanA sinA RHS: 4*sqrt(xy) = 4* sqrt (tanA + sinA)(tanA – sinA) = 4* sqrt(tan 2 A – sin 2 A) = 4* sqrt(sin 2 A/cos 2 A – sin 2 A) = 4*...
 
Y RAJYALAKSHMI 2 days ago
View all Questions »