Second derivative of the position function/first derivative of the velocity function
Absolute value of velocity
This theorem guarantees absolute maximum and minimum values (if f(x) is continuous on a closed interval)
F'(x) changes from + to - , or f'' < 0
An extension of MVT, this theorem guarantees f'(c) = 0
This theorem states that f'(c) = aroc (if f(x) is contin on a closed interval and differentiable on open interval)
F''(x) is negative or f'(x) is decreasing
Down
F''(x) is positive or f'(x) is increasing
To get these: f'(x) = 0 or where f'(x) is undefined
Largest y-value to critical point/endpoint of the domain
Points of _ are found by solving where f''(x) = 0 or is undefined. F''(x) changes sign here
The steps for this process include: creating 2 equations, substituting, finding critical points, and justifying.
First derivative of the position function
Smaller y-value to critical point/endpoint of the domain
If f'(x) > 0
F'(x) changes from - to + , or f'' > 0
If f'(x) < 0
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It prints on two pages.
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