Question

If the total cost function is given by; C = 5x³+ 2x²+ 7, find the average cost and marginal cost when x = 4.

Answer 1

The cost function is given by,

C = 5x³ + 2x² + 7.

Average cost when x = 4 is given by,

$= \frac{C(4) \: -C \: (0)}{4 - 0}$

C(4) = 5(4)³ + 2(4)² + 7 = 5(64) + 32 + 7

C(0) = 5(0) + 2(0) + 7

Now,

$\sf{Average\:cost} \\ \\ = \frac{5(64) + 32 + 7 - 7}{4} \\ \\ = \frac{5(64) + 32}{4} \\ \\ = \frac{4(80) + 4(8)}{4} \\ \\ = 80 + 8 \\ \\ = \boxed{ \boxed{88}}$

Marginal cost is (dC/dx) at x = 4

Finding dC/dx :

dC/dx = d/dx(5x³ + 2x² + 7)

dC/dx = 15x² + 4x

At x = 4,

Marginal cost = 15(4)² + 4(4) = 15(16)+ 16 = 256.

Answer 2

The cost function is given by,

C = 5x³ + 2x² + 7.

Average cost when x = 4 is given by,

= 4−0

C(4)−C(0)

C(4) = 5(4)³ + 2(4)² + 7 = 5(64) + 32 + 7

C(0) = 5(0) + 2(0) + 7

Now,

= 45(64)+32+7−7

= 45(64)+32

= 44(80)+4(8)

=80+8

= 88

Marginal cost is (dC/dx) at x = 4

Finding dC/dx :

dC/dx = d/dx(5x³ + 2x² + 7)

dC/dx = 15x² + 4x

At x = 4,

Marginal cost = 15(4)² + 4(4) = 15(16)+ 16 = 256.