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First Derivative test
Turning points (set equal to zero) - put y back into original equation to find the y coordinate
Turning points can also be stationary points
Looking for a minimum and a maximum
if f’ is larger than zero then there is a maximum
If f’ is smaller that zero then there is minimum
How do you find a local maximum
Find the first derivate, if larger that zero then there is a local maximum
How do you find a local minimum
Find the first derivative, if smaller than zero then there is a local minimum
Global Minimum
The value of y is the smallest attained in the functions domain
Global maximum
The value of y is the greatest attained on the entire domain
Local maximum
A TURNING POINT where the gradient (slope) is positive
Local minimum
Where the TURNING POINT (going to be on a gradient) has a negative sign
(Test) The second derivative
To find the points of inflection
Find the maxima and minima
Using concavity - determined on positive or negative to the direction of concavity
How do you know if your function is concave up (local minimum)
If f’’ is smaller that 0 then there is a local minimum (a minimum on a concavity)
How do you know if your function is concave down
f’’ will be larger than zero (you will have a local maximum)
What do you do if f’’ is = 0
Inconclusive - look the first derivative f’
Inflection points
Corresponds to a change in concavity - placed where there is a change in concavity
Concave down (from inflection point)
When f’’ is smaller than zero
Concave up (from inflection point)
When f’’ is larger than 0
Horizontal point of inflection
When f’ =0 the slope (gradient) is parallel to the x axis
