Leaving Cert Ordinary Level Maths LCOL Differentiation

LCOL Differentiation

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Lessons in this topic

All 7 lessons.

1Introduction 2The Second Derivative 3Shapes of Derivatives 4Using Differentiation to find the slope 5Slope of a tangent to a curve 6Turning Point of a Function 7`Rates of Change

Key ideas in this topic

★ Must learn

f ‘(x) = the slope

The derivative of a function is its slope. To find the slope of a curve, differentiate; for the slope at a particular point, substitute that point’s x-value. A positive slope goes up, a negative slope goes down.

LCOL Differentiation 4

Slope of tangent = slope of curve

At the point of contact, the tangent’s slope equals the curve’s slope — so differentiate the curve and substitute the x-value of the contact point.

LCOL Differentiation 5

★ Must learn

Distance → velocity → acceleration

Differentiate distance to get velocity (speed); differentiate again — distance twice — to get acceleration. ‘Rate of change’ always means differentiate.

LCOL Differentiation 7