Question 1 (1 point)

Question

The cost, c(x), in dollars per hour of running a trolley at an amusement park is
modelled by the function c(x) = 2.1x* - 12.7x + 167.4
+, Where x is the speed in kilometr
hour. At what approximate speed should the trolley travel to achieve minimum

Answer 1

To find the speed at which the cost function \( c(x) = 2.1x^2 - 12.7x + 167.4 \) achieves its minimum, we can use the formula for the vertex of a parabola, since the cost function is a quadratic function.

The vertex \( x \) coordinate of a quadratic function \( ax^2 + bx + c \) can be found using the formula:

\[ x = -\frac{b}{2a} \]

Here, \( a = 2.1 \) and \( b = -12.7 \).

Now, plug in the values:

\[ x = -\frac{-12.7}{2 \times 2.1} = \frac{12.7}{4.2} \]

Calculating this gives:

\[ x \approx 3.02 \]

Thus, the trolley should travel at approximately 3.02 kilometers per hour to achieve minimum running costs.