Answer:
4.2
Step-by-step explanation:
Given the distance between the pendulum and the base of the
clock, f(x), over the horizontal distance, x, modeled by
the function shown.
f(x) = 0.25x² – 2x + 10
In order to get the minimum distance between the pendulum and the base of the clock, first, we need to find the turning point of the function.
At turning point, d{f(x)}/dx = 0
d{f(x)}/dx = 0.5x-2 = 0
0.5x = 2
x = 2/0.5
x = 4
Then we will substitute x = 4 into the function as shown;
f(4) = 0.25(4)²-2(0.4)+10
f(4) = 4-9.8+10
f(4) = 4.2
The minimum distance between the pendulum and the base of the clock is 4.2
