New Zealand
Level 8 - NCEA Level 3

# Functions from rate of change

## Interactive practice questions

A rate of change function is given by $\frac{dx}{dt}=\sqrt{t}+t^5$dxdt=t+t5 :

Determine $x\left(t\right)$x(t). Use $C$C as the constant of integration.

Easy
Approx 3 minutes

A rate of change function is given by $\frac{dy}{dx}=\left(4x+\frac{1}{x}\right)\left(5x-\frac{2}{x}\right)$dydx=(4x+1x)(5x2x):

Determine $y\left(x\right)$y(x) given that $\frac{dy}{dx}=9-\frac{1}{\sqrt{x}}$dydx=91x and $y=4$y=4 when $x=16$x=16.

Use $C$C as the constant of integration.

### Outcomes

#### M8-11

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

#### 91579

Apply integration methods in solving problems