Question Tag: Differentiation

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  • 9 Marks

QT – May 2017 – L1 – Q3a – Elements of Calculus

Differentiate a cost function and determine how quickly the cost is changing at a specific production level.

The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

Where x is measured in number of units and  in GH¢.

Required:

i) Calculate the derivative of  with respect to .
(5 marks)

ii) Determine how quickly the cost is changing at x=1000
(4 marks)

  • 10 Marks

QT – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

Renes Trading Company sells qq kente strips per month at pp Ghana Cedis per kente strip. The demand function for kente strips is given by p=300−0.02qp = 300 – 0.02q. The kente strips cost GH¢30 per strip to manufacture. There are fixed costs of GH¢9,000 per month.

Required:
(i) Determine the price per kente strip that will maximize revenue. (4 marks)
(ii) Determine the quantity where profit is maximized. (4 marks)
(iii) Calculate the maximum profit. (2 marks)

(i)

 

ii)

 

iii)

 

  • 2 Marks

QT – Nov 2018 – L1 – Q2a – Elements of Calculus

Define the stationary point of a differentiable function of one variable.

What is a Stationary Point of a differentiable function of one variable?

A stationary point of a differentiable function of one variable is a point in the domain of the function where the derivative is zero. Equivalently, the slope of the graph at that point is zero.

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