# Functions and their graphs

1. f(x)=X3-3X2+5 (-1,3)

I need to find local Maxima and Local Minima for this Question. Also determine where the function is increasing and where it is decreasing. round answer to two decimal places.

2. g(x)= X2+1

(a) Find the average rate of change from -1 to 2.

(b) Find an equation of the secant line containing (-1,g(-1) ) and (2,g(2) ).

3. If f(x)= -3x if x<-1

0 if x= -1

2x2+1 if x>-1

Find (a) f(-2) (b) f(-1) (c) f(0)

For above question sketch the graph of each function. Be sure to label 3 points on the graph.

https://brainmass.com/math/graphs-and-functions/functions-graphs-326054

#### Solution Preview

1. f(x)=X^3-3X^2+5

I need to find local Maxima and Local Minima for this Question. Also determine where the function is increasing and where it is decreasing. round answer to two decimal places.

Solution:

To find the critical points, find f'(x) and equate it to 0.

f'(x) =

Put f'(x) = 0

= 0

3x(x - 2) = 0

=>x = 0, 2

Let us check for maxima or minima

Let us find f"(x)

f"(x) = 6x - 6

f"(0) ...

#### Solution Summary

Functions and their graphs are evaluated. An equation of the secant line containing a function are determined.