1800 2000 838

CART 0

• 0

MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price:

There are no items in this cart.
Continue Shopping
                   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


3 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

9 months ago

More Questions On Differential Calculus

Post Question

Vouchers
To Win!!!
​Q. IF f ( x ) IS A DIFFERENTIABLE FUNCTION AND f ’ ( x ) = log 1/3 ( log 3 ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .

Ans: Hello Student, Please find answer to your question below If the f(x) is decreasing, then ............(1) Also for the domain of logarithm function, …......(2) Combining (1) and...

 Jitender Singh 7 months ago

but i think a > 4 as a =3 doesnt satisfy the equation.

 bharat makkar 7 months ago
evaluate the limit in image where [ ] is the greatest integar and | | moduls

Hello student, Your question is not clear and seems to be incomplete. Please recheck your question and post it again so that I can provide a meaningful answer.

 Latika Leekha 17 days ago
tangents and normals find the equation of the tangent to the curve x= sin 3t , y=cos 2t at t=pi/4

Ans: Hello Student, Please find answer to your question, …..........(1) …..........(2) Divide (2) by (1) This is slope of tangent. Point is Equation is:

 Jitender Singh 7 months ago
Find the equation of the line passing through the point (2,3) and at a distance of 3 units from the origin.

let eqn. of line be y-3=m(x-2), where m is slope of line dist. from origin = 3 I0-3-m(0-2)I/(1+m 2 ) 1/2 =3 solving we get , m=0 or -12/5 lines are y=0 or 5y+12x=39

 Abhishek Singh 2 months ago
∫cos(2 cot-1​​{ root(1-x/1+x)} = ????