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AP Calculus Unit 2

Derivative instantaneous rate of change / slope of the tangent line
when g'(x) > 0... g(x) is increasing
when g(x) is increasing... g'(x) > 0
when g'(x) < 0... g(x) is decreasing
when g(x) is decreasing... g'(x) < 0
when g(x) has an extrema... g'(x) = 0
when g'(x) = 0... g(x) has an extreme
Power Rule 1) multiply LC of term by exponent -- 2) sutbract 1 from the exponent
Derivative Of Sine Is... cosine
Derivative Of Cosine Is... -sine
Root To Exponent inside / outside
Horizontal Tangent f'(x) = 0 -- slope of tangent line is 0
Critical Values Give Us... possible relative extrema
How To Create Sign Graph 1) find derivative of equation -- 2) set equation equal to zero to get critical values -- 3) put critical values on graph -- 4) plug in number in each interval to find pos or neg value
Maximum Of g(x) Occurs When... g'(x) goes from + to -
Minimum Of g(x) Occurs When g'(x) goes from - to +
When Using Trig On Sign Graphs identify where values will be positive or negative using unit circle
Tangent Line Equation y1-y2 = m (x1-x2)
To Make A Tangent Line Equation, You Need... a point & a slope
A Double Root Indicates... the sign does not change
Horizontal Tangent Is The Same As Saying... Critical Values
Only Plug Into The Original Equation To Find... a y value
How To Calculate Slope y1-y2 / x1-x2
Normal Line (didn’t review) line perpendicular to the tangent line at the point of tangency
Created by: abievans
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