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


2 years ago

Share

                                        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 & RegardsJitender SinghIIT DelhiaskIITians Faculty

2 months ago

More Questions On Differential Calculus

Post Question

Vouchers
To Win!!!
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

 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 &...

 Jitender Singh 2 months ago

Ans: Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty

 Jitender Singh one month ago

 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...

 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.