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:
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Answer:
4.8ft
Step-by-step explanation:
Oksuru k diyaf ramincok ani kasilm asiyla olusan bir refle kstir.
You do -2 plus 4. Answer is 2.
Then do 2-(-2) which is 0.
The final answer is 2.
Explanation
We must the tangent line at x = 3 of the function:
The tangent line is given by:
Where:
• m is the slope of the tangent line of f(x) at x = h,
,
• k = f(h) is the value of the function at x = h.
In this case, we have h = 3.
1) First, we compute the derivative of f(x):
2) By evaluating the result of f'(x) at x = h = 3, we get:
3) The value of k is:
4) Replacing the values of m, h and k in the general equation of the tangent line, we get:
Plotting the function f(x) and the tangent line we verify that our result is correct:
Answer
The equation of the tangent line to f(x) and x = 3 is:
