Find the local maxima and local minima, if any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows.
g(x)=x2+2x,x>0
Given function is, g(x)=x2+2x,x>0
⇒g′(x)=12+2(−1x2)=12−2x2 and g"(x)=−2(−2)x−3=4x3
For maxima or minima put, g'(x)=0
⇒12−2x2=0⇒12=2x2⇒2=4⇒x=2,−2 [∵x>0 (given)]
At x=2, g"(2)=423=48=12>0
∴x=2 is a point of minima.
Minimum value, g(2)=22+22=1+1=2