Assignment:
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)=2x3-4x2+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 t 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).
Provide complete and step by step solution for the question and show calculations and use formulas.