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Grade 12

Secant to Tangent

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
7min

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

Easy
6min

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

Easy
7min

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

Medium
6min
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Outcomes

12F.D.1.7

Make connections, through investigation, between the slope of a secant on the graph of a function (e.g., quadratic, exponential, sinusoidal) and the average rate of change of the function over an interval, and between the slope of the tangent to a point on the graph of a function and the instantaneous rate of change of the function at that point

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