6.2 Summary and exercises

Average gradient: summary and exercises

• The average gradient between two points is: $$\frac{y_2-y_1}{x_2-x_1}$$
• The average gradient of a straight-line function is the same over any two intervals on the function
• The average gradient of a parabolic function depends on the interval and is the gradient of a straight line that passes through the points on the interval
• We can extend the concept of average gradient to any function

End of chapter exercises

1. An object moves according to the function $d=2t^2+1$ , where $d$ is the distance in metres and $t$ the time in seconds. Calculate the average speed of the object between 2 and 3 seconds. The speed is the gradient of the function $d$
   
2. Given: $f\left(x\right)=x^3-6x$ . Determine the average gradient between the points where $x=1$ and $x=4$ .
   
3. Find the average gradient of each of the following functions between the points where $x=2$ and $x=3$
   1. $f\left(x\right)=x^2+3$
   2. $f\left(x\right)=\frac{4}{x}+1$
   3. $f\left(x\right)=2^x-3$