(a) To find the net change, we need to evaluate f(z) at both z = -2 and z = 0 and subtract the two values.
At z = -2:
f(-2) = 3 - 4(-2)^2
= 3 - 4(4)
= 3 - 16
= -13
At z = 0:
f(0) = 3 - 4(0)^2
= 3 - 4(0)
= 3 - 0
= 3
Net change = f(0) - f(-2)
= 3 - (-13)
= 3 + 13
= 16
Therefore, the net change between the given values of the variable is 16.
(b) To find the average rate of change, we need to divide the net change by the difference in the values of the variable.
Difference in values of the variable = 0 - (-2) = 2
Average rate of change = Net change / Difference in values of the variable
= 16 / 2
= 8
Therefore, the average rate of change between the given values of the variable is 8.
A function is given.
f(z) = 3 − 4z2; z = −2, z = 0
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
1 answer