find the average rate of change of f(x)=-x^2+4x+2 from x=3 to x=7
simplify your answer as much as possible
To find the average rate of change of the function f(x)=-x^2+4x+2 from x=3 to x=7, we need to calculate the difference in the function values at these two points and divide it by the difference in the x-values.
First, let's find the value of f(x) at x=3:
f(3) = -(3)^2 + 4(3) + 2 = -9 + 12 + 2 = 5
Next, let's find the value of f(x) at x=7:
f(7) = -(7)^2 + 4(7) + 2 = -49 + 28 + 2 = -19
Now, let's calculate the average rate of change using the formula: (f(7) - f(3)) / (7 - 3)
= (-19 - 5) / (7 - 3)
= -24/4
= -6
Therefore, the average rate of change of f(x) from x=3 to x=7 is -6.