Question

question 25 (1 point)
the cost, c(x), in dollars per hour of running a trolley at an amusement park is modelled by the function c(x)=1x² - 1.2x + 16.4, where x is the speed in kilometres per hour. at what approximate speed should the trolley travel to achieve minimum cost?
a) about 5 km/h
b) about 4 km/h
c) about 3 km/h
d) about 2 km/h

Explanation:

Step1: Find the derivative

Given $c(x)=1x^{2}-10x + 167$, using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, the derivative $c^\prime(x)=2x-10$.

Step2: Set the derivative equal to zero

To find the critical points, set $c^\prime(x) = 0$. So, $2x-10 = 0$.

Step3: Solve for x

Add 10 to both sides: $2x=10$. Then divide by 2, we get $x = 5$.

Answer:

A. about 5 km/h