Question

Calculate the rate of change for the quadratic function over the given interval: f\left( x \right) = {x^2} + 4x + 5;\; - 1 \le x \le 2f(x)=x 2 +4x+5;−1≤x≤2 1 5 2 -4

Answer 1

Answer: The rate of change is 5.

Step-by-step explanation:

Our equation is:

f(x) = x^2 + 4x + 5

And we want to find the rate of change in the range −1≤ x ≤2

when we want to find the rate between x1 ≤ x ≤ x2

we have:

Rate = (f(x2) - f(x1))/(x2 - x1)

So we have:

Rate = ( f(2) - f(-1))/(2 - 1)

Rate = (2^2 + 4*2 + 5 - (-1)^2 - 4*(-1) - 5)/3 = 15/3 = 5

The rate of change is 5.