Graphical Differentiation
Lesson 3.5
The Derivative As A Graph
Given function f(x)
How could we construct f '(x)?
• Note slope values for various values of x
• Recall that we said the derivative is also a
function
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The Derivative As A Graph
Note the graphs of f(x) and f '(x)
f(x)
f '(x)
zero
slope
zero
slope
positive slope
negative slope positive slope
Interesting observation
• If f(x) is a degree three polynomial ...
• What does f '(x) appear to be?
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Caution
When you graph the derivative
• You are graphing the slope of
the original function
• Do not confuse slope of original with y-value
of the original
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Graphing Derivatives
Original function may have oddities
• Points of discontinuity
• Not smooth, has corners
Thus the derivative will also have
discontinuities
Sketch the
derivative of
this function
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Can You Tell Which?
Given graphs of two functions
• Which is the original function?
• Which is the derivative?
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Assignment
Lesson 3.5
Page 220
Exercises 1 – 17 odd
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