Medal for anyone who answers and ill become a fan . what is the end behavior asymptote for 2x^2/x+3. Please answer

Question

anonymous · Answer

2x-6

kmeezy · Answer

can you show the way you got the answer? i have more questions like this and i want to solve them by myself @ijakez

anonymous · Answer

kmeezy · Answer

thankss

loser66 · Answer

Do you know derivative?

kmeezy · Answer

yes @Loser66

loser66 · Answer

oh, good, 
Take the first derivative and solve for critical value

loser66 · Answer

you will have x =0 and x =-6 are critical value.
But x =-3 is asymptote Hence, f(0) is local min and f(-6) is local max

loser66 · Answer

Moreover, the value of the function is < 0 when x <-3, right? because the numerator >0 for all x

loser66 · Answer

and value of the function is >0 when x > -3
That give us : for critical value x =-6 (its max), the graph is |dw:1459726463967:dw|

loser66 · Answer

|dw:1459726550019:dw|