the derivative
Post on 06-Aug-2015
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{The Derivative
Slope of a line, secant line, tangent line, slope of a secant line, slope of a line tangent to a curve
Lines, slope, point-slope form
What do we know about slopes of lines?
Lines, slope, point-slope form
Lines, slope, point-slope form
Lines, slope, point-slope form
Lines, slope, point-slope form
Given a curve, the line that intersects the curve on two points is called a secant line.
Secant line
Given a curve, the line that intersects the curve on two points is called a secant line.
Secant line
Tangent line
Given a non-linear curve, how do you get the slope of the curve at a the point (x, f(x) )?
Challenge question
Given a non-linear curve, how do you get the slope of the curve at a the point (x, f(x) )?
Challenge question
Let be the slope of the tangent line, then the slope of the curve at (x,f(x)) is the same as is the derivative of f at x. ๐ โฒ (๐ฅ )=๐๐๐ฟ
๐ฆ= ๐ (๐ฅ )
How do we compute
Challenge question
How to find
(๐ฅ ๐ , ๐ (๐ฅ ๐ ) ) ๐๐๐ฟ=ฮ๐ฆฮ๐ฅ
=๐ฆ2โ ๐ฆ1๐ฅ2โ๐ฅ2
๐ โฒ (๐ฅ )= limฮ๐ฅโ 0
๐ (๐ฅ+โ ๐ฅ )โ ๐ (๐ฅ )โ๐ฅ
Three step rule1. Find 2. Find
3. Evaluate
How to compute for
limฮ๐ฅโ0
๐ (๐ฅ+โ๐ฅ )โ ๐ (๐ฅ )โ ๐ฅ
How to compute for
First step
How to compute for
Second step
How to compute for
Third step
๐ โฒ (๐ฅ )=4 ๐ฅโ3
What is
๐ โฒ (2 )=4 (2 )โ3=5
What is
๐ โฒ (0 )=4 (0 )โ3=โ3
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