4346 Local Maximum and Minimum Values The graph of a functio

43-46 Local Maximum and Minimum Values The graph of a function f is given. Use the graph to estimate the following (a) All the local maximum and minimum values of the function and the value of x at which each occurs. (b) The intervals on which the function is increasing and on which the function is decreasing.

Solution

a) Local maxima : at point before which f(x) is increasing after maxima f(x) is decreasing

Local minima : at point before which f(x) is decreasing and aftre local minima f(x) is increasing

Local maxima : ( -2, 2) ; Local Minima :( 0 , -1)

Local maxima : ( 2,1)

b) Interval of increase : ( - inf , -2) U ( 0, 2))

Interval of decrease ( -2 , 0) U ( 2, inf)