Final answer:
The value of t corresponding to the highest point on the curve is t = 2, and the value of the function at this point is 4.
Step-by-step explanation:
To find the value of t corresponding to the highest point on the curve, we need to find the maximum value of the y-coordinate. The y-coordinate of the curve is given by the equation y(t) = 4t - t².
To find the maximum value, we can first find the derivative of the equation y(t) and set it equal to zero. Derivative of y(t) with respect to t is y'(t) = 4 - 2t.
Setting y'(t) = 0, we get 4 - 2t = 0. Solving for t, we find t = 2.
Substituting t = 2 into the equation y(t), we get y(2) = 4(2) - (2)² = 8 - 4 = 4.
Therefore, the value of t corresponding to the highest point on the curve is t = 2, and the value of the function at this point is 4.