Minimum, maximum critical points of functions

Question

Determine intervals on which the function is increasing, decreasing, and which critical points are a relative minimum, maximum. 

 

Given function: h (x)= 2x-8/ x+7

Answer 1

 

Hint:

 

Find the first derivative of h(x) which is h'(x)

 

If h'(x) is not defined/does not exist for x = c then you have a critical point at x=c

 

To check if x=c is a relative maximum or relative minimum or neither evaluate h(x) for x=c

 

If h(x) is not defined/does not exist for x=c then you have neither relative maximum nor relative minimum at x=c

 

 

To determine if it is increasing or decreasing you have to consider two intervals in this case (-∝,c) and (c,∞)

If h'(x)>0 for all x on those intervals then h(x) is increasing on those intervals.