Monotonicity (AOD)
is there any other way of doing this problem other than manually keeping values in f'(x) as x=0,1 to check if it's increasing or decreasing in that interval
I understand they're checking f'(x)=0 at some point alpha to know that there exists a local minima at that point, but how would I know if that is the only point of local minima? how can I be sure that the curve will not meet again at x-axis after intersecting x-axis?
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@Apu
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Have you heard of Intermediate value theorem? @BlindSniper (BS)
yeah f(x) from [a,b] is f(a)+f(b)/2 something like that
but how is that relevant to this problem?
No this is not
If f(a)*f(b) < 1
Then f is zero for atleast one x between a and b
oh
but then from that you'll only know that it's increasing after local minima and it reaches x-axis
my doubt is how would you know if it's not going to touch the x-axis again?
Ok bro
*0
Wait isn't it something like if f(a).f(b)<0 then function is zero at least one point?
Or do I need to revise calc? :sweaty:
Oh yeah right
yeah exactly my bad i wrote f’
Am I like dumb to think we can solve by a lengthiet method of taking e^x as t and solve
but that's what we did?
Isse idea lelo thodha
Mera solve krha hua h
oh wait
if f'(t) only has 1 root then it's only changing direction once
therefore it only passes through x-axis once
bruh am I retarded how did I not think of that
thanks anyway
+solved @Aman
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