Instantaneous rate of change homework

[abordel]

Homework Statement

For the function f(x)=3x^2-1, for what x values is the instantaneous rate of change equal to the average rate of change on the interval [1,3]

Homework Equations

The Attempt at a Solution

 

[tnutty]

1) first find the average rate of change on the interval (1,3)

2) set that number equal to the derivative of the function and solve for x1) Finding the avg rate of change over the interval 1,3

f(1) = 2
f(3) = 26

so we have (1,2) and (3,26)
the slope give the rate of change so to find the slope between these points
we use the slope formula which gives us 12

2) f `(x) = 3x^2+1

average rate of change = 6x

12 = 6x

x = 2

so when x = 2 in the instantaneous rate of change, it equals the average rate on the
interval [1,3]. notice its between 1 and 3.

 

[Feldoh]

Just to add you might want to look-up the mean value theorem.