Differentiation

NZ Level 7 (NZC) Level 2 (NCEA)

Deriving the Power Rule

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

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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

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