The cost C (in dollars) of manufacturing x wheels at Deon's Bicycle Supply is given by the function C(x)= 0.1x^2-60x+22,744. What is the minimum cost of manufacturing wheels? Do not round your answer.
as you know the vertex of a parabola is at x = -b/2a, so here the minimum is at
x = 60/0.2 = 300
So, figure C(300)
For the function f ( x ) =3x+2/5 , find the difference quotient f(a+h)-f(a)/H
To find the minimum cost of manufacturing wheels, we need to determine the vertex of the quadratic function C(x).
The function C(x) is in the form of a quadratic equation: C(x) = ax^2 + bx + c, where a = 0.1, b = -60, and c = 22744.
The x-value of the vertex is given by the formula x = -b / (2a). Let's calculate that:
x = -(-60) / (2 * 0.1)
x = 60 / 0.2
x = 300
The x-value of the vertex is 300. To find the corresponding y-value, we substitute x = 300 into the equation C(x):
C(300) = 0.1(300)^2 - 60(300) + 22744
= 9000 - 18000 + 22744
= -9000 + 22744
= 13744
Therefore, the minimum cost of manufacturing wheels is $13,744.