Suppose that f(x)=3x^3+3x. Find all critical values of f. Then use interval notation to state when f(x) is increasing and when f(x) is decreasing and to state when f(x) is concave up and concave down. Find the local maxima and local minima. Find all vertical and horizontal asymptotes as well as all inflection points.

Question

Suppose that f(x)=3x^3+3x.  Find all critical values of f.  Then use interval notation to state when f(x) is increasing and when f(x) is decreasing and to state when f(x) is concave up and concave down.  Find the local maxima and local minima.  Find all vertical and horizontal asymptotes as well as all inflection points.

Steve · Answer

f' = 9x^2+3 f" = 18x max/min when f' = 0 increasing when f' > 0 concave up when f" > 0 Now go for it.