Question

PLEASE HELPP AM GIVING MORE POINTS THAN I SHOULD FOR THIS

a pebble is tossed into the air from the top of a cliff. the height, in feet, of the pebble over time is modeled by the equation y=-16x² + 32x + 80.
What is the maximum height in feet reached by the pebble?​

Answer 1

y = 80 ft

Explanation:

The height will be maximum at the point where the derivative of y with respect to x becomes zero. So, first we will take derivative of the equation with respect to x:

dy/dx = (d/dx)(-16 x² + 32 x + 80)

dy/dx = -32 x + 32

Now, we set it equal to zero:

dy/dx = 0 = - 32 x + 32

32 x = 32

x = 32/32

x = 1

Therefore, height will be maximum at x = 1. So, we put x = 1 in equation:

y = -32(1)² + 32(1) + 80

y = 80 ft