Concepts Flashcards
Approximations of trapezoidal rule:
Based on concavity. Concave up is an over approximation, and concave down is under.
How to determine the units of a derivative (ex. of f(x)) :
df / dx = units of f(x) / units of x
The Big Four you should include when interpreting f’ (and the sentence format to help with this):
context of f(x), rate of change, instant (x-value), and units
at x= ___, the _(context of f(x) ___ is increasing/decreasing at a rate of ____ (units).
If a function’s slopes are decreasing, the tangent line is ____. In other words, ___.
If a function’s slopes are increasing, the tangent line is ____. In other words, ____.
an overestimate, it’s concave down
an underestimate, it’s concave up
NOTE: it’s not about positive or negative slopes, it’s about if the values are getting steeper or not
When a function has a point of inflection, f’(x) ____, or f’‘(x) ____.
goes from increasing to decreasing or vice versa (positive or negative doesn’t matter)
goes from being positive to negative or vice versa