New Zealand
Level 8 - NCEA Level 3

# The Derivative as a Limit - Limiting Chord Process

## 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

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

Consider the function $f\left(x\right)=4^x$f(x)=4x

Consider the function $f\left(x\right)=-x^2+5$f(x)=x2+5

### 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