3. Applications of differentiation
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
2min
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)=2.3x−0.003x2
Easy
1min
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
Easy
2min
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
Easy
3min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account