NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Small changes and marginal rates

## Interactive practice questions

The cost $C$C, in dollars, of producing $x$x items of a product, is modelled by the function $C\left(x\right)=1300+7x+0.002x^2$C(x)=1300+7x+0.002x2

a

Determine the marginal cost function.

b

Hence calculate the marginal cost, $C'\left(90\right)$C(90), when $90$90 items have already been produced.

Easy
Approx 3 minutes

The profit $P$P, in dollars, from producing and selling $x$x items is modelled by the function $P\left(x\right)=2.3x-0.003x^2$P(x)=2.3x0.003x2

The revenue $R$R, in dollars, earned from selling $x$x items is modelled by the function $R\left(x\right)=-0.02x^2+40x+4000$R(x)=0.02x2+40x+4000

The cost $C$C in dollars, of producing $x$x diodes is modelled by the function $C\left(x\right)=12x+\frac{18050}{x}$C(x)=12x+18050x

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems