NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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Review Rate of Change

Interactive practice questions

Consider the function $f\left(x\right)=2x^2$f(x)=2x2

a

By filling in the table of values, complete the limiting chord process for $f\left(x\right)=2x^2$f(x)=2x2 at the point $x=1$x=1.

$a$a $b$b $h=b-a$h=ba $\frac{f\left(b\right)-f\left(a\right)}{b-a}$f(b)f(a)ba
$1$1 $2$2 $1$1 $\editable{}$
$1$1 $1.5$1.5 $\editable{}$ $\editable{}$
$1$1 $1.1$1.1 $\editable{}$ $\editable{}$
$1$1 $1.05$1.05 $\editable{}$ $\editable{}$
$1$1 $1.01$1.01 $\editable{}$ $\editable{}$
$1$1 $1.001$1.001 $\editable{}$ $\editable{}$
$1$1 $1.0001$1.0001 $\editable{}$ $\editable{}$
b

The instantaneous rate of change of $f\left(x\right)$f(x) at $x=1$x=1 is:

Easy
Approx 8 minutes
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Consider the function $f\left(x\right)=4^x$f(x)=4x

Consider the function $f\left(x\right)=x^3$f(x)=x3

The population of koalas in a particular area can be modelled by the equation $y=11+2^x$y=11+2x, where $x$x is the number of years from now.

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

91578

Apply differentiation methods in solving problems

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