#1**+3 **

**(a)** Here's a graph: https://www.desmos.com/calculator/fxto5gtfns

**(b)** P = (2, 8) Q = (x, x^{3})

Find the slope of the line PQ for the following values of x .

When x = 1.5, Q = (1.5, 1.5^{3}) = (1.5, 3.375)

We want to find the slope of the line passing through the points (2, 8) and (1.5, 3.375)

slope = \(\frac{8-f(1.5)}{2-1.5}\,=\,\frac{8-3.375}{2-1.5}\,=\,\frac{4.625}{0.5}\,=\,9.25\)

This is the first value for the slope of the secant on the table.

x | m_{sec} | |

1.5 | 9.25 | |

1.9 | \(\frac{8-f(1.9)}{2-1.9}\,=\,\frac{8-6.859}{2-1.9}\,=\,\frac{1.141}{0.1}\,=\,11.41\) | |

1.99 | \(\frac{8-f(1.99)}{2-1.99}\,=\,\frac{8-7.880599}{2-1.99}\,=\,\frac{0.119401}{0.01}\,=\,11.9401\) | |

2 | ? | |

2.01 | \(\frac{8-f(2.01)}{2-2.01}\,=\,\frac{8-8.120601}{2-2.01}\,=\,\frac{-0.120601}{-0.01}\,=\,12.0601\) | |

2.1 | \(\frac{8-f(2.1)}{2-2.1}\,=\,\frac{8-9.261}{2-2.1}\,=\,\) |

Do you see how I am doing these? See if you can finish the table...

**(c)**

The slope of the tangent line when x = 2 appears to be between 11.9401 and 12.0601

Let's just take the average of these two... (11.9401 + 12.0601) / 2 = 12.0001

So I'd guess that the slope of the tangent line at (2, 8) is 12

hectictar
Oct 21, 2017

#1**+3 **

Best Answer

**(a)** Here's a graph: https://www.desmos.com/calculator/fxto5gtfns

**(b)** P = (2, 8) Q = (x, x^{3})

Find the slope of the line PQ for the following values of x .

When x = 1.5, Q = (1.5, 1.5^{3}) = (1.5, 3.375)

We want to find the slope of the line passing through the points (2, 8) and (1.5, 3.375)

slope = \(\frac{8-f(1.5)}{2-1.5}\,=\,\frac{8-3.375}{2-1.5}\,=\,\frac{4.625}{0.5}\,=\,9.25\)

This is the first value for the slope of the secant on the table.

x | m_{sec} | |

1.5 | 9.25 | |

1.9 | \(\frac{8-f(1.9)}{2-1.9}\,=\,\frac{8-6.859}{2-1.9}\,=\,\frac{1.141}{0.1}\,=\,11.41\) | |

1.99 | \(\frac{8-f(1.99)}{2-1.99}\,=\,\frac{8-7.880599}{2-1.99}\,=\,\frac{0.119401}{0.01}\,=\,11.9401\) | |

2 | ? | |

2.01 | \(\frac{8-f(2.01)}{2-2.01}\,=\,\frac{8-8.120601}{2-2.01}\,=\,\frac{-0.120601}{-0.01}\,=\,12.0601\) | |

2.1 | \(\frac{8-f(2.1)}{2-2.1}\,=\,\frac{8-9.261}{2-2.1}\,=\,\) |

Do you see how I am doing these? See if you can finish the table...

**(c)**

The slope of the tangent line when x = 2 appears to be between 11.9401 and 12.0601

Let's just take the average of these two... (11.9401 + 12.0601) / 2 = 12.0001

So I'd guess that the slope of the tangent line at (2, 8) is 12

hectictar
Oct 21, 2017

#2**+3 **

See i was doing this exact thing, but why does that formula have the (4), where does it come from? Other than thanks for the break down, i was trying to figure this out, and if it wasnt for that for it would have been fine. cause no matter what i put in it it, i was getting answer of 1.

Veteran
Oct 21, 2017