Differentiation

New Zealand

Level 7 - NCEA Level 2

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

Loading Graph...

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

Easy

< 1min

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

Easy

3min

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

Easy

1min

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

Easy

1min

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