Answer:
See Explanation
Explanation:
A. f(x) = -16x² +24x + 16
0 = -8(2x² - 3x - 2) ⇒ -8(2x + 1)(x - 2) = 0 ⇒ x = -1/2, 2
B. f'(x) = -32x + 24 ⇒ 0 = -8(4x - 3) ⇒ x = 3/4
f''(x) = -32 ⇒ f''(3/4) = -32 ⇒ concave down ⇒ maximum
f(3/4) = -16(9/16) + 24(3/4) + 16 = -9 + 18 + 16 = 25
By the second derivative test, the point (3/4, 25) is a maximum.
C. 1. Plot the intercepts. 2. Plug in points. 3. Draw the curve.