This document discusses differentiation and finding gradients and stationary points. It explains that differentiation is the rate of change of a quantity with respect to another, and the power rule is used to apply differentiation. Gradients can be found through differentiation by taking the first differential of a curve's equation using the power rule and evaluating it at given points. Stationary points occur when the gradient is zero, and the nature of turning points as maxima, minima or points of inflection can be determined. Completing the square is another method demonstrated for finding turning points of quadratic functions.

1. Differentiation

2. What is Differentiation
• Rate of Change of a quantity with respect to another quantity
• Speed
• Acceleration
• Gradient

3. Applying Power Rule

4. Solve the following using power rule

5. Finding Gradient through differentiation
• Gradient can be found using differentiation using the power rule.
• Use the equation of the curve and first find the first differential using
the power rule.
• Then, input the value of coordinates and find the gradient at that
point.

6. Example
• Find the gradient of the curve

7. Find the Gradients of the curve at the points mentioned

8. What are Stationary Points?

9. More about stationary points

10. Finding stationary points
• Find the stationary points of the function

11. Find the turning points of the following
curves

12. Finding Nature of Turning Points

13. Nature of Turning Points Exercise
• Find the turning points and define the nature of the turning points.

14. Finding turning Points using completing the
square

15. Turning Points Using Completing the Square

16. Completing the Square to find turning points
• Complete the square of the following to find the turning points