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                   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

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                                        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

one year 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...

 Jitender Singh one year 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 one year ago
Why is equation (1) not a polynomial equation and equation (2) not a polynomial in y? (1) dy/dx + sin(dy/dx) = 0 (2) (dy/dx) 2 +(dy/dx) - sin 2 y = 0

Being a equation and a polynomial equation is very different. Functions like sinx, lnx, e x are not considered polynomial quations. They are transcental functions.

 Nibir Pawan Das 11 months ago

@Yugabrat sinx=0 is also a equation..

 Shibashis Mallik 11 months ago

As sin is present...

 Yugabrat Gogoi 11 months ago
Differentiate x arcsin (x) w.r.t arcsin(x)

HInt: Try to assume arcsin(x) = z and then try to differenciate it. Also please remember that z is also the function of x. Thanks.

 Vijay Mukati one month ago
Two sides rhombus ABCD are parallel to the lines y=x+2 and y=7x+3.if the diagonals of the rhombus intersect at the point(1,2)& the vertex A is on yhe y axis,find the possible coordinates of ...

The answer should be c=0,2.5 Assume A(0,c). Now opposite sides in rhombus are parallel and all sides are equal length. Or to check if a quardilateral is rhombus, it is sufficient to show...

 Akshay one month ago

Alternative solutions will be to use vectors, Let A(0,c). Assume side length=d. AC will be = (1-0) i +(2-c) j, Line AD can be in 1 st or 2 nd quardent, Point B = (0 i + c j) + d/rt(2) * (i...

 Akshay one month ago
If the distance between circumcentre and orthocentre of triangle whose vertices are (1,5) (2,3) (4,4) is k/√10 then sum of abscissa of points which are k distance away from the point (3,2)...

A (1,5) B (2,3) C (4,4) AB= √5 units BC=√5 units AC= √10 units Hence given triangle is right angled triangle ( AB2 + BC2 = AC2) at B Orthocenter is B only CIrcumcenter for...

 Harsh Patodia 11 months ago
prove that the triangle which has one of the angles as 60 degree, can not have all vertices with integral coordinates

If we take origin and two arbitrary coordinates with lines passing through them. calculate slope. slope difference between can not be 60.

 Charchit Tailong 28 days ago
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