Question

Estimate the value of the function f(x) = 4x + 4 over the interval [0, 5].

a) 4
b) 8
c) 12
d) 16

Answer 1

To estimate the value of the function f(x) = 4x + 4 over the interval [0, 5], substitute the endpoints into the function and calculate the corresponding values. The estimated value of the function over the interval [0, 5] is 24.

Step-by-step explanation:

To estimate the value of the function f(x) = 4x + 4 over the interval [0, 5], we substitute the endpoints of the interval into the function and calculate the corresponding values.

For x = 0, f(0) = 4(0) + 4 = 0 + 4 = 4.

For x = 5, f(5) = 4(5) + 4 = 20 + 4 = 24.

Since the function is linear and the interval is [0, 5], the function starts at 4 and increases by 4 units for every 1 unit increase in x. Therefore, f(0) = 4 and f(5) = 24. The estimated value of the function over the interval [0, 5] is 24.