Chapter 4: Applications of Differentiation Flashcards
The Mean Value Theorem
The idea that, should you have points A and B with a slope of D between them on a function both continuous and differentiable at all points between A and B, there will be a point C at which f’(C) = D.
Rolle’s Theorem
The idea that, should you have both points A and B with a slope of zero between them on a function continuous and differentiable at all points between A and B, there will be a point C at which f’(C) = 0.
Maximum & Minimum Values
At points at which f’(x) = 0, the function f(x) is at a maximum or minimum value.
Local Minimum/Maximum
The lowest/highest point on a specified interval.
Absolute Minimum/Maximum
The lowest/highest point on a function.
L’Hospital’s Rule
When both limits are approaching the same point and are indeterminate form of type (0/0) or (inf/inf), then the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
Indeterminate Function
When it isn’t obvious at first glance what the derivative will be due to a struggle between the numerator and denominator.
To use L’Hospital’s theorem, turn a function into a ___.
Quotient
To solve using L’Hospital, you can apply a ___ to the entire equation, and then plug the calculated limit into said ___ equation and solve.
Natural log; natural log.
When choosing what goes on top with L’Hospital, it’s typically best to put the ___ in the numerator.
Logarithm
To solve an optimization problem, create ___ for each distance that you need to calculate. Divide each by the corresponding ___, add the two together, and set them equal to the total T. Then, ___ (which should be set equal to ___) and solve for x.
Equations; rate; take the derivative; zero.
Even functions have ___ symmetry.
Reflectional
Odd functions have ___ symmetry.
Rotational
