Homework Soursea Find the intervals of increase or decrease b find the loca
(a) Find the intervals of increase or decrease. (b) find the local maximum and minimum. (c) Find the intervals of concavity and the inflection points. (d) Use the information from parts (a)-(c) to sketch the graph. Check your work with a graphing device if you have one.
f(x)=36x+3x^2-2x^3
f(x)=36x+3x^2-2x^3
Solution
f\'=1-sint=0 for crit t=-3pi/2,pi/2 f\"=-cost however f\" at these 2 points are both 0 , and f\' is always +ve , so it is increasing all the time f\"=0 t=-3pi/2.-pi/2,pi/2,3pi/2are inflection points as they changes sign concave up[-2pi,-3pi/2)(-pi/2,pi/2)(3pi/2,2pi] concave down are the rest min at t=-2pi max at t=2pi
