# Tangent line

Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points.

The function to define is

F(x)=2x^3-4x^2+3x-5

The possible tangent lines are:

y= x-5

y= 2x-5

y= 3x-5

a) what is/are the zero(es) for this function? In other words, what is the solution for:

f(x)= 0

b) what axes values (x- and y- ranges) are appropriate for this graph?

c) when plotting each linear function with f(x), which line appears to be tangent to the curve at the point

1) (0,-5)

2) How about at (1,-4)

D) What are thederivatives f'(0) and f'(1), and how do they relate to the slopes of the tangent lines to these points?

E) Find a function for the normal line to the curve at the point (0,-5).

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#### Solution Preview

The solution is attached below. If you have any question, please let me know. Thank you.

Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points.

The function to define is

F(x)=2x^3-4x^2+3x-5

F'(x) = 6x2 - 8x + 3

The possible tangent lines are:

y= x-5

y= 2x-5

y= 3x-5

a) what is/are ...

#### Solution Summary

This provides an example of working through a specified process to find tangent line for a function.