Match the expression with its name. 9X4 - 3x + 4 A. cubic binomial
B. quadratic monomial
C. not a polynomial
D. fourth-degree trinomial

Find the maximum height by solving for when the derivative of f(x) = 0 and the sign changes from positive to negative:

f(x) = -16x² + 2x + 48

Find the derivative of each term:

f'(x) = -32x + 2

Set the equation equal to 0:

0 = -32x + 2

-2 = -32x

x = 1/16 sec

Validate that the derivative changes from + to - at this value by plugging in values into the derivative formula on both sides of 1/16:

f'(0) = 2, +

f'(2) = -62, -

Therefore, there is a maximum at x = 1/16 because the function changes from positive to negative. Find the height at x = 16 seconds. (Plug it into the original equation)

f(1/16) = -16(1/16)² + 2(1/16) + 48

f(1/16) = -1/16 + 2/16 + 48

f(1/16) = 1/16 + 48

f(1/16) = 48 1/16 or 48.0625 ft

Round to nearest hundredth: ≈48.06 feet.