Question

Am I correct? Please show your work so I can compare it to my work. Thank you!

Answer 1

Answer:

200

Step-by-step explanation:

C = 0.007x² − 2.8x + 100

There are two ways we can find the minimum.  The first is by noticing that this is an upwards parabola, so the minimum is at the vertex.  For y = ax² + bx + c, the vertex is at x = -b/(2a).

x = -(-2.8) / (2 × 0.007)

x = 200

Alternatively, we can minimize C using calculus.  Take the derivative with respect to x and set to 0:

dC/dt = 0.014x − 2.8

0 = 0.014x −  2.8

x = 200