



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 straightline 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
 An object moves according to the function
$d=2{t}^{2}+1$ , 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
$d$
 Given:
$f\left(x\right)={x}^{3}6x$ .
Determine the average gradient between the points where
$x=1$ and
$x=4$ .
 Find the average gradient of each of the following functions between the points where
$x=2$ and
$x=3$

$f\left(x\right)={x}^{2}+3$

$f\left(x\right)=\frac{4}{x}+1$

$f\left(x\right)={2}^{x}3$
Source:
OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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