The cost, c(x) in dollars in per hour of running a certain fishing boat is modeled by the function c(x)= 0.9x^2 - 18.1x + 135.1, where x is the speed in km/hour/ At what approximate speed should the boat travel to achieve minimum cost?
clearly the minimum cost is at the vertex of the parabola, which is at x = -b/2a = 18.1/1.8
To find the speed at which the boat should travel to achieve minimum cost, we need to determine the vertex of the function.
The function c(x) = 0.9x^2 - 18.1x + 135.1 is a quadratic function in the form of ax^2 + bx + c.
The x-coordinate of the vertex of a quadratic function with equation f(x) = ax^2 + bx + c is given by the formula x = -b/2a.
In this case, a = 0.9 and b = -18.1. Plugging these values into the formula, we get:
x = -(-18.1) / (2 * 0.9)
x = 18.1 / 1.8
x ≈ 10.06
Therefore, the boat should travel at an approximate speed of 10.06 km/hour to achieve the minimum cost.
To find the approximate speed at which the boat should travel to achieve the minimum cost, we need to determine the x-value that corresponds to the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).
In our given function c(x) = 0.9x^2 - 18.1x + 135.1, we can identify that a = 0.9, b = -18.1, and c = 135.1.
Using the formula, the x-coordinate of the vertex is:
x = -(-18.1) / (2 * 0.9)
= 18.1 / 1.8
= 10.06
Therefore, the approximate speed at which the boat should travel to achieve minimum cost is around 10.06 km/hour.