Test review please help

Question

Answer 1

(9)

The Profit function is P(t) = 1500t - 3√t - 50,000.

Average rate of change in profit is given by .

Average rate of change in profit between 3 months and 7 months.

P(3) = 1500*3 - 3√3 - 50,000

P(3) = 4500 - 5.1961 - 50,000

P(3) = -45505.196

P(7) = 1500*7 - 3√7 - 50,000

P(7) = 10500 - 7.9372 - 50000

P(7) = -39507.93

Average rate of change in profit between 3 months and 7 months is

Therefore Average rate of change in profit between 3 months and 7 months is 1499.3147.

Answer 2

(10)

The function is x(t) = t² - 7t + 12.

Instantaneous rate of change in x(t) is the derivative of the function

Apply derivative on both side

x'(t) = 2t - 7*1 + 0

x'(t) = 2t - 7

Instantaneous rate of change in x(t) is zero.

 2t - 7 = 0

2t = 7

t = 7/2

t = 3.5

Therefore for t = 3.5, the Instantaneous rate of change in x(t) is zero

Answer 3

(11)

The Volume of the cube with length of side x is v(x) = x³

Instantaneous rate of change in volume of the cube is the derivative of the voume of the cube.

Apply derivative on both side

d(v(x))/dt = 3x²

Therefore instantaneous rate of change in volume of the cube is 3x².