To find the values of a and b, we can use the given information about the function f(x) and its derivatives at x = 0.
First, we know that the value of f(0) is 1, which means that when we plug x = 0 into the function, we get f(0) = 20 + a0 + b*0^2 - 0 + 2 = 1. Solving this equation for b, we get b = -1.
Next, we know that the derivative of the function f(x) at x = 0 is ƒ'(0) = 1. The derivative of a polynomial function is given by ƒ'(x) = 2x + ax + bx^2 - 1. Plugging in x = 0, we get ƒ'(0) = 20 + a0 + (-1)*0^2 - 1 = 1. Solving for a, we get a = 1.
Therefore, the values of a and b are a = 1 and b = -1. The sum of these values is a + b = 1 + (-1) = 0.
Explanation:
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The possible values for the missing number that make the given expression the square of a binomial is; 81
<h3>Binomial Expression</h3>
We are given the expression;
x² + 18x
- Now, if we consider the binomial; x ± b
Squaring that gives us;
x² ± 2ax + b²
Comparing this expression to the one we are given we can say that;
±2ax = 18x
±a = 18/2
a = ±9
Thus,we will have;
(x + 9)² as our expression which is;
x² + 18x + 81
Therefore, the missing number is 81.
Read more on binomial expression at; brainly.com/question/14968861
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