Answer:
a. 28.
b 20.78.
Explanation:
a. f(x) = 0.001(x - 10)(x + 20)(x - 40)
When x = 50
Height = f(40) = 0.001(50-10)(50+20)(50-40)
= 0.001(40*70*10)
= 0.001 * 28,000
= 28 units.
b.
Expanding the function we get
f(x) = 0.001(x - 10)(x^2 - 20x - 800)
f(x) = 0.001(x^3 - 30x^2 - 600x + 8000)
f(x) = 0.001x^3 - 0.03x^2 - 0.6x + 8
Finding the derivative
f'(x) = 0.003x^2 - 0.06x - 0.6
This is zero for maxm/minm values:
0.003x^2 - 0.06x - 0.6 = 0
x = 27.32, - 7.32.
The values of the heights corresponding to these values of x are:
0.001(27.32-10)(27.32+20)(27.32-40)
= -10.39. and
0.001(-7.32-10)(-7.32+20)(-7.32-40)
= 10.39.
So the distance between A and B = 10.39 - (-10.39)
= 20.78.