A question about a derivative and simplifying...

Question

anonymous · Answer

$$\frac{ x-x^2 }{ 2-3x+x^2 }$$

anonymous · Answer

Use product rule

hartnn · Answer

factorise denominator

anonymous · Answer

This is the same question that you gave for vertical asymptotes

anonymous · Answer

Arent we suppose to find derivative

anonymous · Answer

$$\frac{ (2-3x+x^2)(1-2x)-(x-x^2)(-3+2x) }{ (2-3x+x^2)^2 }$$

hartnn · Answer

u can first simplify , then derivate

anonymous · Answer

Factorize denominator and then cancel the like terms on num and den
then use produvt rule

anonymous · Answer

what!!!

anonymous · Answer

i can do that!!!!!!?????

hartnn · Answer

u notice x-1 can be cancelled.?
ofcourse u can do that

anonymous · Answer

factor then find derivative!!!!!!!??????

anonymous · Answer

write 2-3x+x^2 as (x-1)(x-2) first

anonymous · Answer

yes

anonymous · Answer

wow, i have spent hours on this problem D;

hartnn · Answer

x/(x-2) = x(x-2)^{-1}
now differentiate

anonymous · Answer

ok i got it now thanks you guys :)

anonymous · Answer

it is -x/(x-2) @hartnn I guess you made a typo

hartnn · Answer

yup.

anonymous · Answer

if that is the first derivative, how did they get 1 as a critical point?

anonymous · Answer

this is so frustrating

hartnn · Answer

i don't think 1 is a critical point....

anonymous · Answer

Critical points are the points where f^1(x) is zero or f^1(x) is not defined

anonymous · Answer

but 1 is good...its not a critical point

anonymous · Answer

Ok, the book says the graph increases from (-inf,1),(1,2),(2,inf)

hartnn · Answer

anonymous · Answer

thats good...it shows the same..1 is not a critical point

anonymous · Answer

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