Flashcards
Differentiation
Cards in this deck (10)
- 1What is differentiation used for?Finding instantaneous rates of change
- 2Define differentiation\[f'(x)=\lim\limits_{h\to0} \frac{f(x+h) - f(x)}{h}\]
- 3Differentiation from first principlesSubstitute \(f(x)\) and \(f(x + h)\)for actual function then simplify
- 4Find tangent and normal from differentiationUse differentiation to find the gradient of the tangent at a point then substitute to find the equation of the tangent
For the normal, take the negative reciprocal of the gradient and then substitute - 5Basic formula for gradient function\[f(x) = ax^n \Rightarrow f'(x) = anx^{n-1}\]
- 6What is a stationary point?A point where \(\frac{\mathrm{d}y}{\mathrm{d}x} = 0\)
- 7How to find stationary pointsFind derivative
Let derivative equal 0
Solve for values
Substitute - 8Nature of stationary points (no 2nd derivative)Check derivatives of integer values either side of the point in question
-ve -> +ve = minimum point
+ve -> -ve = maximum point - 9What is the second derivative?The derivative of the derivative
(found by differentiating the gradient function) - 10Sketch the gradient function from a graphTurning points on graph = roots on a graph of the gradient
+ve gradient on graph = gradient function above the axis
-ve gradient on graph = gradient function below the axis
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- A level OCR A level Maths (Calculus) Flashcards on Differentiation, created by James Norman on 31/12/2018.
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- James Norman
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