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Tangent line

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

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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 ...

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