5 Written questions
5 Matching questions
- Intermediate Value Theorem
- Fundamental Theorem of Calculus #1
- ln(cscx+cotx)+C = -ln(cscx-cotx)+C
- Square root function
- First Derivative Test for local extrema
- b If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k
The definite integral of a rate of change is the total change in the original function.
5 Multiple choice questions
This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
Yes f' decreases on X<C so f''<0
f' increases on X>C so f''>0
A point of inflection happens on a sign change at f''
5 True/False questions
Fundamental Theorem of Calculus #2 →
ln(sinx)+C = -ln(cscx)+C →
Critical Number → If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)
f is continuous at x=c if... →
Mean Value Theorem →
The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.