EasyMathematicsHigh School (11–12)Functions and Calculus › Application of DerivativesNumericalA-Level AP Board Exam IB

A small factory in Leeds makes bicycle helmets…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A small factory in Leeds makes bicycle helmets. The cost of making $x$ helmets in one day is

\displaystyle C(x) = 0.002x^3 - 0.3x^2 + 40x + 2000 \text{ pounds}.

Find the marginal cost when $x = 50$ . Then find the actual extra cost of making the 51st helmet, and compare the two.

Need a reminder? The key ideaShow

The derivative $\dfrac{dy}{dx}$ is the rate of change of $y$ with respect to $x$ , in units of $y$ per unit of $x$ . For a particle, $v = \dfrac{ds}{dt}$ and $a = \dfrac{dv}{dt}$ . The marginal cost is $C'(x)$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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