Interactive practice questions
Consider the function $f\left(x\right)=x^2$f(x)=x2
a
By filling in the table of values, complete the limiting chord process for $f\left(x\right)=x^2$f(x)=x2 at the point $x=3$x=3.
| $a$a | $b$b | $h=b-a$h=b−a |
$\frac{f\left(b\right)-f\left(a\right)}{b-a}$f(b)−f(a)b−a |
|---|---|---|---|
| $3$3 | $4$4 | $1$1 | $\editable{}$ |
| $3$3 | $3.5$3.5 | $\editable{}$ | $\editable{}$ |
| $3$3 | $3.1$3.1 | $\editable{}$ | $\editable{}$ |
| $3$3 | $3.05$3.05 | $\editable{}$ | $\editable{}$ |
| $3$3 | $3.01$3.01 | $\editable{}$ | $\editable{}$ |
| $3$3 | $3.001$3.001 | $\editable{}$ | $\editable{}$ |
| $3$3 | $3.0001$3.0001 | $\editable{}$ | $\editable{}$ |
b
The limiting chord process has been used to calculate the instantaneous rate of change for each value of $x$x given in the table. Complete the missing values.
| $x$x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
|
Instantaneous rate of change of $f\left(x\right)$f(x) at $x$x. |
2 | 4 | $\editable{}$ | 8 | $\editable{}$ |
c
We can therefore deduce that the instantaneous rate of change of $f\left(x\right)$f(x) at any point $x$x is:
Easy
6min
Consider the function $f\left(x\right)=2x^2$f(x)=2x2
Easy
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Consider the function $f\left(x\right)=3x+2$f(x)=3x+2.
Easy
2min
Consider the function $f\left(x\right)=8-x$f(x)=8−x.
Easy
1min
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