Concepts

Question 1

Approximations of trapezoidal rule:

Answer 1

Based on concavity. Concave up is an over approximation, and concave down is under.

Question 2

How to determine the units of a derivative (ex. of f(x)) :

Answer 2

df / dx = units of f(x) / units of x

Question 3

The Big Four you should include when interpreting f’ (and the sentence format to help with this):

Answer 3

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).

Question 4

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, ____.

Answer 4

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

Question 5

When a function has a point of inflection, f’(x) ____, or f’‘(x) ____.

Answer 5

goes from increasing to decreasing or vice versa (positive or negative doesn’t matter)
goes from being positive to negative or vice versa