Given the function f, of, x, equals, minus, x, squared, minus, 3, x, plus, 5f(x)=−x
2
−3x+5, determine the average rate of change of the function over the interval minus, 3, is less than or equal to, x, is less than or equal to, 4−3≤x≤4.
To find the average rate of change over the interval [-3, 4], we first need to find the values of the function at x = -3 and x = 4.
1. When x = -3:
f(-3) = -(-3)^2 - 3(-3) + 5
f(-3) = -9 + 9 + 5
f(-3) = 5
2. When x = 4:
f(4) = -4^2 - 3(4) + 5
f(4) = -16 - 12 + 5
f(4) = -23
The average rate of change is given by (f(4) - f(-3))/(4 - (-3)).
Substitute the values we found:
= (-23 - 5)/(4 + 3)
= (-28)/7
= -4
Therefore, the average rate of change of the function over the interval [-3, 4] is -4.