Find the net change in the value of the function between the given inputs.
g(t) = 8 − t2; from −6 to 9
To find the net change in the value of the function between the given inputs, we need to calculate the difference between the function values at the endpoints of the interval.
1. Evaluate the function at the lower endpoint (-6):
g(-6) = 8 - (-6)^2
= 8 - 36
= -28
2. Evaluate the function at the upper endpoint (9):
g(9) = 8 - 9^2
= 8 - 81
= -73
3. Calculate the net change:
Net change = g(9) - g(-6)
= -73 - (-28)
= -73 + 28
= -45
Therefore, the net change in the value of the function g(t) between -6 and 9 is -45.
To find the net change in the value of the function between the given inputs, we need to evaluate the function at the endpoints and then subtract the smaller value from the larger one.
First, let's evaluate the function at the lower input of -6:
g(-6) = 8 - (-6)^2 = 8 - 36 = -28.
Next, let's evaluate the function at the upper input of 9:
g(9) = 8 - 9^2 = 8 - 81 = -73.
Now, we can calculate the net change by subtracting the smaller value from the larger one:
Net change = g(9) - g(-6) = -73 - (-28) = -73 + 28 = -45.
Therefore, the net change in the value of the function between the inputs -6 and 9 is -45.
45
that would be just how much g changed:
g(9) - g(-6)
just plug in the values for t and do the math.