Answer:
The maximum value of the function is 3.
Step-by-step explanation:
Given;
f(x) = -3(x-4)(x - 6)
f(x) = -3[x² - 6x - 4x + 24]
f(x) = -3[x² - 10x + 24]
f(x) = -3x² + 30x - 72
a = -3, b = 30, c = -72
For maximum point: a < 0
For minimum point: a > 0
Since a = -3, the function has maximum points
The maximum points = (x , y)
x = -b/2a
x = -30/(2 x -3)
x = -30/-6
x = 5
y = f(-b/2a) = f(5)
f(5) = -3(5)² + 30(5) - 72
f(5) = -75 + 150 - 72
f(5) = 3
Therefore, the maximum value of the function is 3.
