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Calculus and Analytical
Geometry
MTH 104
Lecture#14
Derivatives
Fauzia Bibi and Sarah Amjad
Mathematics Department,
COMSATS University Islamabad, Wah Campus
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REVIEW OF LAST LECTURE
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Tangent lines and rates of change
Slope of the tangent line
Displacement and average velocity
Rate of change
Instantaneous Velocity
TOPICS TO BE COVERED
• The derivative
• Equation of tangent line using derivative
• Differentiable function
• Points of non differentiability
• Differentiability implies continuity
• Other derivative notations
OBJECTIVES
• To learn the derivative of a function
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The Derivative of a Function
Example 1:
Solution:
HOW TO FIND THE EQUATION OF
TANGENT LINE:
Example 3:
Differentiable Function
POINTS OF NON DIFFERENTIABILITY
• corner points
• points of vertical tangency
• Points of discontinuities
Points of
discontinuity
Example 5:
Differentiability Implies Continuity
But the converse is not true, i
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For example,
The function
is continuous
at x=0, but not
differentiable