# Determine the relationship between the rates of change of f and g. ?

## The equation represents the function f, and the graph represents the function g. f ( x ) = 6x - 5 Determine the relationship between the rates of change of f and g. The rate of change of g is twice the rate of change of f. The rate of change of f is the same as the rate of change of g. The rate of change of f is 3 times the rate of change of g. The rate of change of f is twice the rate of change of g.

Jun 19, 2018
$$The rate of change of f is twice the rate of change of g.


#### Explanation:

The rate of change of $f$ can be found from the given expression for $f$. This shows that

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(6 x - 5\right) = 6$

To find the rate of change of $g$, we have to use two suitable points on the graph (as the graph is a straight line, any pair should return the same value for the slope). It can be seen that the graph for $g$ goes through the points $\left(- 1 , - 1\right)$ and $\left(1 , 5\right)$. Thus the rate at which $g$ increases is

$\frac{5 - \left(- 1\right)}{1 - \left(- 1\right)} = \frac{6}{2} = 3$