Carlos's claim that the maximum value of the function is 4 is correct.
Carlos's claim that the maximum value of the function is 4 is correct. To verify this, we need to find the critical points of the function and analyze the behavior of the function at these points.
The function given is:
h(t) = -16t² + 128t + 4
First, we need to find the critical points by taking the derivative of the function with respect to t and solving the resulting equation:
h'(t) = -32t + 128
Critical points:
t = 4 (from h'(t) = 0)
Now, we need to analyze the behavior of the function at these critical points:
t = 4:
At this point, the function attains a local maximum, as the derivative is 0 and the value of the function is 4.
Since there is only one critical point, and the function attains a maximum value at this point, Carlos's claim that the maximum value of the function is 4 is correct.