1. The price function for a product is p(t) = (60 - 3/t) and the demand function

Question

1. The price function for a product is p(t) = (60 - 3/t) and the demand function is x(t) = (1200 - 0.05t2). Find R'(t) when t=80

2. If f(x) = x( 6 +e3x) find the value of f'( 1.5 ). Give the answer correct to two decimal places.

3. In order to boost sales, Quink Inc introduces a new line of Pink Quinks. The revenue equation is given by R(x) = 75 4. x2e-0.09x. What is the maximum revenue? Give your answer correct to 2 decimal places.

5. If f(x) = e3.0x / (1+ 3 x) find the value of f'( 0.3 ). Give the answer correct to two decimal places.

6. If f(x) = (1+e3.5x)(1-e2x) find the value of f'( 0.3 ). Give the answer correct to two decimal places.

7. If f(x) = x2( 14 -e1-2x) find the value of f'( 1.6 ). Give the answer correct to two decimal places.

8. Due to the phenomenal success of Zinc Pink Quinks, a website dedicated to them is set up. Management wishes to know is sales are related to how many times a day people click on the Zinc Pink Quink Link. It is found8 that demand is given by the equation x = - 102 log(t/ 19 ), where t is the number of clicks per day measured in thousands. If sales are 172 per day how many clicks can be expected per day? Give your answer to the nearest whole number

Explanation / Answer

1. p(t) = (60 - 3/t)

x(t) = (1200 -0.05t2)

R(t) = p(t)*x(t) = (1200 -0.05t2)*(60 - 3/t)

R'(t) = (-0.1t)*(60 - 3/t) +(1200 -0.05t2)*(3/t^2)

R'(80) = (-0.1*80)*(60 - 3/80) +(1200 -0.05*80^2)*(3/80^2) = -479.2875

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