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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

10 months ago

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Ans: There is some little mistake in the expression Differentiete one time & apply the chain rule ….....(1) Put in (1)

 Jitender Singh 10 months ago

Dear student, This is a formula for nth order differentiation. Can you please elaborate what is the second step that you want to be clarified. You need to specify whether you like to do an...

 Sumit Majumdar 9 months ago

sumit sir ….….…i understood this question ….…..................but i have another question can u please tell me my problem ….….…....the question is please explain fully ….if it has 0/0 form...

 milind 9 months ago
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kindly post ur question again to get it bee answered

 ng29 20 days ago

Your question is incomplete plzz review it again

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Dear student, Please post the correct question. Thanks Nishant Vora

 Nishant Vora 25 days ago

where is the question kindly post it again to get it be answered

 ng29 25 days ago
curve 16x 2 +8xy+y 2 -74x-78y+212=0 represents parabola ellipse hyperbola none of these

yes it is parabola for parabola h 2 =ab and also Discriminant must be non zero Discriminant= abc+2fgh-af 2- bg 2 -ch 2 for given eq- a=16 b=1 h=4 approve if useful

 ng29 23 days ago

@neeraja check ur answer again u had written a=4 and that is incorrect according to ur values answer is not parabola

 ng29 23 days ago

parabola! h=4 a=4 b=1 h^2=ab which implys parabola study short cut methods on parabola

 Neeraja Outdare 23 days ago
what will the graph of |x| + [x] look like?

Dear student, You can break the defination of the function in various intervals |x| + [x] = and so on then plot in respective interval

 Nishant Vora 26 days ago
Plese solve the following integral ∫|x| dx Limit is from -1 to 2.