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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


4 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

if y=log(tan x) the value of dy/dx = ….......................................................

y=log(tan x) dy/dx = d(log(tanx))/dx = (1/tanx) *d(sinx/cosx)/dx = (cosx/sinx) * (cosx/-sinx) = – (cosx*cosx) / (sinx*sinx) = – cos 2 x/sin 2 x Hope it helped

 Jigar Marvaniya 8 days ago
if x 2 +xy+3y 2 =1 then find (x+6y) 3 d 2 y/dx 2 +22(x 2 +3y 2 )=0

Hii I am giving you hint how to proceed. Use it and even if you are not able to contact us .

 Sourabh Singh 7 days ago
what is the differentiation????????????????????????????????????????????

Dear Sudharashan Packing can be a source of product is called differentiation. This will be usefull in mathematics as well as physics

 Prabhakar ch 3 months ago

hi sudarshan... Differentiation (economics), the making a product different from other similar products. Differentiation (ethnography), the invention of ostensible differences between...

 manichandra 3 months ago

hi sudarshan... Differentiation (economics), the making a product different from other similar products. Differentiation (ethnography), the invention of ostensible differences between...

 mohan 3 months ago
integrate the following:- how to integrate the following function limits are from 0 to pi/4 ∫dx÷(cos^3x (2sin2x) 1/2 )

Put tanx = t , we get sec^2x dx = dt

 BALAJI ANDALAMALA 3 months ago
Find the vector equation of the plane through the points (2, 1, –1) and (–1, 3, 4) and perpendicular to the plane x – 2y + 4z = 10.

You need to consider normal to a plane as (a,b,c). You have 2 coplanar vectors and normal to the plane with the help of which you can find the value of a, b ,c .

 Sourabh Singh one month ago

Sir, I tried to do it............but got stuck up in the middle........... can u please solve it......!!!!

 Smruthi one month ago
what are some important value we can earn in studying arithmetic progression and geometric progression

Understanding AP and GP will let you understand how the series can be solved easily which increases or decreases by the fixed ratio or distance. Thanks

 Vijay Mukati 10 months ago
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