##### Edexcel 8MA0/01 Jun 2024 AS Exam Q. 12 : 13 marks in 15:36 min.

##### Edexcel 8MA0/01 May 2024 AS Mock Q. 11 : 9 marks in 10:48 min.

##### Edexcel 9MA0/02 Jun 2023 A2 Exam Q. 1 : 4 marks in 4:48 min.

##### Edexcel 8MA0/01 Jun 2023 AS Exam Q. 1 : 6 marks in 7:12 min.

##### Edexcel 8MA0/01 Apr 2023 AS Mock Q. 13 : 12 marks in 14:24 min.

##### Edexcel 9MA0/02 Jan 2023 A2 Mock Q. 6 : 7 marks in 8:24 min.

##### Edexcel 8MA0/01 Jun 2022 AS Mock Q. 10 : 8 marks in 9:36 min.

##### Edexcel 8MA0/01 Jun 2022 AS Exam Q. 12 : 12 marks in 14:24 min.

##### Edexcel 9MA0/02 Nov 2021 A2 Exam Q. 5 : 7 marks in 8:24 min.

##### Edexcel 8MA0/01 Oct 2020 AS Exam Q. 14 : 9 marks in 10:48 min.

##### Edexcel 9MA0/02 Mar 2020 A2 Mock Q. 7 : 7 marks in 8:24 min.

##### Edexcel 9MA0/01 Jun 2019 A2 Exam Q. 12 bcd : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 Jun 2019 A2 Shadow Exam Q. 12 bcd : 6 marks in 7:12 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Exam Q. 13 : 10 marks in 12:00 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Shadow Exam Q. 13 : 10 marks in 12:00 min.

##### Edexcel 8MA0/01 Jun 2019 AS Exam Q. 5 : 5 marks in 6:00 min.

##### Edexcel 9MA0/02 Jan 2019 A2 Mock Q. 3 : 9 marks in 10:48 min.

##### Edexcel 9MA0/01 Jun 2018 A2 Exam Q. 2 : 7 marks in 8:24 min.

##### Edexcel 8MA0/01 Jun 2018 AS Exam Q. 8 : 9 marks in 10:48 min.

##### Edexcel 8MA0/01 May 2018 AS Mock Q. 1 : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 May 2018 A2 Mock Q. 11 : 10 marks in 12:00 min.

##### Edexcel 8MA0/01 Jun 2017 AS Sample Exam Q. 15 : 8 marks in 9:36 min.

##### Edexcel 8MA0/01 Jun 2017 AS Sample Exam Q. 16 : 10 marks in 12:00 min.

##### Edexcel 9MA0/01 May 2017 A2 Sample Exam Q. 1 : 7 marks in 8:24 min.

##### Edexcel 9MA0/02 May 2017 A2 Sample Exam Q. 14 : 9 marks in 10:48 min.

##### Finding value of 1st derivative at given point

##### Explore tangent and normal to curve

##### Explore where function is increasing and decreasing

##### Explore a stationary point

##### Explore key features linking function and derivative

##### Exploring second derivatives

##### Differentiating Quadratics

*touches*the curve at that point. Such a line is called a

*tangent*. This tangent line will have a gradient.

Drag the red point in the display below to move the tangent line along the quadratic graph, and see how the gradient changes.

You can see that the gradient function f'(x) of a quadratic curve is a straight line.

##### Differentiating Cubics

*touches*the curve at that point. Such a line is called a

*tangent*. This tangent line will have a gradient.

Drag the red point in the display below to move the tangent line along the cubic graph, and see how the gradient changes.

You can see that the gradient function f'(x) of a cubic curve is a quadratic curve.

##### Differentiating Quartics and Higher Order

You can see that the gradient function f'(x) of a quartic curve is a cubic curve.

Finally you can investigate higher order curves. In each case, the gradient function f'(x) will be a curve of one order lower.

##### Gradients of Polynomials Including Negative Indices

You can also set coefficients of negative indices \(x^{-1}\), \(x^{-2}\) and \(x^{-3}\).

Drag the red sample point to help you investigate.

##### Stationary Points - Maxima and Minima

These points are called stationary points. The "top of the hill" of the curve is called a maximum point. The "bottom of the valley" of the curve is called a minimum point.

You can drag the blue sample point to help you investigate.

##### Stationary Points - Maxima and Minima

A sample point, which you can drag to help investigate, is displayed in blue.

Look carefully at the points where the curve becomes horizontal. What is the value of x at these points? These points are called stationary points. The "top of the hill" of the curve is called a maximum point. The "bottom of the valley" of the curve is called a minimum point.

Can you find those points where the gradient is at its greatest? And where the gradient is at its smallest?

##### Points of Inflection

You can drag the blue sample point to help you investigate.

In the display below the graph of y = f(x) is shown for polynomial functions, together with the graphs of y = f'(x) and y = f''(x).

f(x) is initialised to $y = {\left( {x + 1} \right)^3} + 3$ $(= {x^3} - 3{x^2} + 3x + 2)$

This curve has a point of inflexion at x = 1. What are the values of f'(x) and f''(x) at this point?

Once again, you can drag the blue sample point to help you investigate. You can then check your findings with curves of your own.

##### Differentiating ${e^x}$ and ${ln (x)}$

You can change f(x) with the sliders and drag the red sample point.

##### Investigate Differentiation of ${ln (ax)}$

as a changes.

##### An Increasing Function

The function $f\left( x \right) = {x^3}$ has a gradient of zero at $x = 0$

##### A Decreasing Function

##### Increasing or Decreasing?

Identify which of the following 10 curves show increasing or decreasing functions, or neither.

##### Strictly Increasing/Decreasing Functions

The gradient of $f(x) = {x^3} + 1$ is 0 at $x = 0$, but it is still strictly increasing at this point, because to the left $f(x)$ is less, and to the right $f(x)$ is more ($\forall a,b:a < b \Rightarrow f(a) < f(b)$).

The gradient of $f(x) = - {x^3} + 1$ is 0 at $x = 0$, but it is still strictly decreasing at this point, because to the left $f(x)$ is more, and to the right $f(x)$ is less ($\forall a,b:a < b \Rightarrow f(a) > f(b)$).

##### Investigate Trig Differentiation

The graph of the first derivative is shown in red and the graph of the second derivative is in purple.

The x-slider allows you to run along the curves to see correpondence at a single point.

Can you see how the derivative of sin is cos?

Can you see how the derivative of cos is -sin?

Can you see how the derivative of tan is sec

^{2}?