Let f(x) be a polynomial function such that f(−4)=−5,f′(−4)=0 and f′′(−4)=1. classify the point (−4,−5).
1 answer:
You might be interested in
We want to find an equation for the given solutions and the multiplicity of each solution.
The equation is:
First, assume that we have a given equation and we know that we have solutions {x₁, x₂, ..., xₙ}, each one with multiplicity {m₁, ..., mₙ}.
The equation, of a polynomial that meets these requirements, is given by:
Where A is the leading coefficient and can be any real number.
Now that we know that, here we have the solutions:
- x = 2 with multiplicity 2
- x = -1 with multiplicity 2
We don't have information about the leading coefficient, so we assume it is equal to 1.
Then the equation is:
If you want to learn more, you can read:
Answer:
Step-by-step explanation:
How does y change as x increases over a range?
As x increases from -6 to -4, y decreases from 0 to -7
It is a decreasing function in this range and for ranges less than x = -6 as well as the slope is nearly constant
As x increases from -4 to 0, y increases from -7 to 4
It is an increasing function in this range.
For x increasing from zero, y becomes less and less
It is a decreasing function in the range larger than x = 0
