Differentiation

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Review Rate of Change

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

a

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

$a$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 |
---|---|---|---|

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

Apply differentiation methods in solving problems