Question
determine the vertical asymptotes of the graph of function.g(x)=x^3 diveded by 5x^3-x^2-22x
Answers
Reiny
b(x) = x^3/(5x^3 - x^2 - 22x)
= x^2/(5x^2 - x - 22) , after dividing by x , x≠0
f'(x) = (2x(5x^2 - x - 22) - x^2(10x - 1) )/(5x^2-x-22)^2
to have a vertical tangent, the slope must be undefined, that is
the denominator of the above f'(x) must be zero
5x^2 - x - 22 = 0
(5x-11)(x+2) = 0
two vertical asymptotes:
x = 11/5 and x = -2
= x^2/(5x^2 - x - 22) , after dividing by x , x≠0
f'(x) = (2x(5x^2 - x - 22) - x^2(10x - 1) )/(5x^2-x-22)^2
to have a vertical tangent, the slope must be undefined, that is
the denominator of the above f'(x) must be zero
5x^2 - x - 22 = 0
(5x-11)(x+2) = 0
two vertical asymptotes:
x = 11/5 and x = -2