Question

What is the maximum altitude (in ft) attained by the rocket described by the function h(t) = −(1/3)t^3 + 4t^2 − 20t + 29?

a. 120 ft
b. 150 ft
c. 180 ft
d. 200 ft

Answer 1

The maximum altitude attained by the rocket described by the function h(t) = -(1/3)t^3 + 4t^2 - 20t + 29 is 180 ft.

Step-by-step explanation:

To find the maximum altitude attained by the rocket, we need to determine the vertex of the quadratic function h(t) = -(1/3)t^3 + 4t^2 - 20t + 29. The vertex of a parabola represents its maximum or minimum point. In this case, since the coefficient of the t^3 term is negative, the parabola opens downwards, and the vertex represents the maximum altitude.The formula for the x-coordinate of the vertex of a quadratic function is -b/2a. In our case, a = -1/3 and b = 4, so the x-coordinate of the vertex is -4/(2*(-1/3)) = 6. Multiplying this value of t with the function, we have h(6) = -(1/3)(6)^3 + 4(6)^2 - 20(6) + 29 = 180 ft.Therefore, the maximum altitude attained by the rocket is 180 ft (option c).