Help! The slant asymptote of #f(x)=(6x^3-5x^2+3x)/(3x^2-x-14)# intersects f where x=?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Bill Jorgensen
May 19, 2018

#y=2x-1#

x-int: #x= 1/2#

Explanation:

Use polynomial division to divide the numerator by the denominator the result is the line that is your slant asymptote.

#(6 x^3 - 5 x^2 + 3 x)/(3 x^2 - x - 14)#

#6 x^3 - 5 x^2 + 3 x = (2 x - 1) × (3 x^2 - x - 14) + 30 x - 14#

so the line #y=2x-1# is your slant asymptote

the x-int is where #y=0#:

#0=2x-1#

#x= 1/2#

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