Question

If f(x)=
2
x + ax + b
x²-x+2
f(0) = 1 and ƒ'(0) = 1,find a +b

Answer 1

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.