Question

f(x)=x^3+6x^2+9x

find:
x intercepts
vertical asymptotes
horizontal/slant asymptotes
derivative
second derivative
increasing interval
decreasing interval
concave up interval
concave down interval

Answer 1

=x(x^2 +6x+9) = x(x+3)^2 = 0
intercepts: x=0,-3

there are no asymptotes since it is a polynomial

f'(x) = 3x^2 +12x +9 ....(using power rule x^n -> n*x^(n-1) )

f''(x) = 6x +12

function is increasing when f'(x) > 0
function is decreasing when f'(x) < 0

function is concave up when f''(x) > 0
function is concave down when f''(x) < 0

Answer 2

thank you!