NZ Level 7 (NZC) Level 2 (NCEA)
Average Vs Instantaneous Rates of Change

## Interactive practice questions

Consider the function $f\left(x\right)=2$f(x)=2 drawn below.

a

Calculate the average rate of change between $x=3$x=3 and $x=6$x=6.

b

State the gradient of the tangent at the point $x=3$x=3.

Easy
Less than a minute

Consider the function $f\left(x\right)=2x+3$f(x)=2x+3 drawn below.

Consider the function $f\left(x\right)=-\frac{\left(x-8\right)^2}{3}+7$f(x)=(x8)23+7.

Consider the function $f\left(x\right)=-\frac{\left(x-4\right)^2}{2}+6$f(x)=(x4)22+6.

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems