Answer:
f(x) represents the vertical height of the cannon
Step-by-step explanation:
The given function is presented as follows;
f(x) = -0.05·(x² - 26·x - 120)
Given that 'x' represent the horizontal path of the cannon and the function describes the path of the cannon, we have that the vertical height reached by the cannon as it moves along the horizontal path is given as the function f(x)
Therefore, we have;
f(0) = -0.05·(0² - 26×0 - 120) = -0.05 × -120 = 6
f(0) = 6
The starting height of the cannon = 6
The maximum height reached by the cannon is given as follows;
f'(x) = d(-0.05·(x² - 26·x - 120))/dx = -0.05·d(x² - 26·x - 120)/dx = -0.05×(2·x - 26)
f'(x) = -0.05×(2·x - 26)
f'(x) = 0 At maximum height, therefore, we have;
-0.05×(2·x - 26) = 0
(2·x - 26) = 0
2·x = 26
x = 26/2 = 13
x = 13
f(13) = -0.05·(13² - 26×13 - 120) = 14.45
The maximum height = 14.45
Therefore;
f(x) = The vertical height of the cannon
