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India
Class XI

Deriving the Power Rule

Interactive practice questions

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=x2. 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=x3. 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=x4. Then answer the questions that follow.

Easy
1min
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Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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