 Doubt from LCD

is it ABC?

IDK answer. Solution bhj do plz

For first option consider e^\left( \beta x \right)f(x) so by Rolle’s theorem A is true, for B consider e^\left(g(x)\right)f(x) again by Rolle’s theorem its true, For C consider \frac{f(x)}{g(x)} again by rolle’s theorem its true, for D consider f(x)^2-x^2 so the given equation is diff. of this and so it has a root in(a,b).

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@Lavesh @VasuBro @Curious_Monkey
Aise Differentiability wale problms mein usually bohot dikkat hoti hai. Jhan pe function assume Krna hota. How to solve such kind problms in general?
Koi theory hoti hai isse related?

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Answer kya h? Only A? Ya A and C? Ya koi aur combo?     1 Like

Mme to aise kr diya tha… Kyunki given condition
\int_0^1 f(x) dx =0 h… Yaani ki area bounded by f(x) with x axis 0 h… To sbse simplest case me mne ek line assume kr li passing through 1/2,0 and 0,1 se… Usse saare optns check kiye… Sirf A hi arha tha possible answer.

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But jo solution given hai usme function assume krke solve kara hai. Ye to maine v solve kiya tha Mean Value theorem ki feel se. Aur AC marke glt answer le aaya @Devansh_Jain help plz

A part assume a function g(x) = e^x(integral 0 to x f(t) dt) . g(0) = g(1)=0 . Then apply rolles theorem

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Thanks.
For Differentiability problms like this. Kya sabme we assume {e^x} and some other function assume krte hain.
Is this General way of doing Differentiability problems?

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thanks

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I did a blunder. seperated e raised to the power (x+1)ln27 as {e raised to the power (x+1)} + {e raised to the power ln27} 2 Likes