NZ Level 7 (NZC) Level 2 (NCEA) Deriving the Power Rule

## Interactive practice questions

Consider the graph of $y=x$y=x below.

a

What is the gradient of the line at $x=4$x=4?

b

What is the gradient at any value of $x$x?

c

Which of the following is a true statement?

If $f\left(x\right)$f(x) is a linear function, the derivative $f'\left(x\right)$f(x) depends on the value of $x$x.

A

A linear function has a constant gradient.

B

The gradient of a linear function is always $1$1.

C

If $f\left(x\right)$f(x) is a linear function, the derivative $f'\left(x\right)$f(x) depends on the value of $x$x.

A

A linear function has a constant gradient.

B

The gradient of a linear function is always $1$1.

C
Easy
Less than a minute

Use the applet below to explore how the gradient of the tangent changes at different points along $y=x^2$y=x2. Then answer the questions that follow.

Use the applet below to explore how the gradient of the tangent changes at different points along $y=x^3$y=x3. Then answer the questions that follow.

Use the applet below to explore how the gradient of the tangent changes at different points along $y=x^4$y=x4. Then answer the questions that follow.

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems