Deriving the Power Rule
Interactive practice questions
Consider the graph of $y=x$y=x below.
What is the gradient of the line at $x=4$x=4?
What is the gradient at any value of $x$x?
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 linear function has a constant gradient.
The gradient of a linear function is always $1$1.
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.