Determine where the graph of the function is increasing decr

Determine where the graph of the function is increasing, decreasing, concave up, concave down. Then sketch the graph. 18) f(x) = 9x^2 + 72x Please sshow your work

Solution

f\'\'(x)=18>0

HEnce the graph is always concave up (A positive second derivative means graph is concave up)

f\'(x)=18x+72

f\'(x)>0

18x+72>0

x>-4

So for x>-4 the function is increasing

f\'(x)<0 gives

x<-4 , for x<-4 the function is decreasing