- #1

juantheron

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[2] Total no. of real solution of the equation ##e^x = x^3##

My Solution:: [1] Let ##f(x) = e^x## and ##g(x) = x^2##

Now we have use Camparasion Test for derivative

So ##f^{'}(x) = e^x## which is ##>0\forall x\in \mathbb{R}## and ##g^{'}(x) = 2x##

So When ##x<0##. Then ##f(x)## is Increasing function and ##g(x)## is Decreasing function

So exactly one solution for ##x\leq 0##

Now for ##x\geq 1##. Then ##f(x)## is Increasing faster then ##g(x)## . So here curve does not Intersect

Now we will check for ##0<x<1##

I Did not understand have can i check here which one is Increasing faster

so please help me

Thanks