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AB Calc
AB Calc
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1
What is the derivative of ln x?
blnx
x ln x
1/ ln x
1/x
2
1. What is the derivative of \sin x?
sec x
- cos x
sin^-1 x
cos x
3
What does the Extreme Value Theorem guarantee?
Area under the curve is bounded
Absolute max and min on a closed interval
Derivative exists at endpoints
Tangents exist
4
What does the Intermediate Value Theorem guarantee?
A max or min exists
The derivative exists
A value between f(a) and f(b) is achieved
The area under the curve is finite
5
What is the inverse rule for derivatives?
f(g(x)) = x
f\left(x\right)=\frac{1}{\sqrt{g\left(x\right)}}
g’(b) = {1} / {f’(a)}
g(x) = {1}/{f(x)}
6
What is the derivative of tan^(-1) x?
1/abs valvue x (x2 + 1)
1/ root(x+1)
1/ x2 + 1
-1/x2 + 1
7
What does the Fundamental Theorem of Calculus Part 2 allow us to do?
Estimate slope
Differentiate
Evaluate a definite integral using antiderivatives
Graph functions
8
What’s the derivative of a
x
where a > 0?
ax-1
ax
x \ln a
ax \ln a
9
If f is differentiable, it is also:
Discrete
continous
Increasing
decreasing
10
What must be true to apply the mean value theorem?
Function must be continuous and differentiable
Function must be increasing on the closed interval [a,b]
Functions derivative must be positive
Function must be bounded
11
Which rule is used to find the derivative of f(x) = x^3 x sin x?
quotient rule
product rule
chain rule
power rule
12
What is the limit: lim x to 0 sin x /x
0
cos x
1
4/4
13
what is the anti-derivative of 1/x
\ln\left|x\right|
\ln \left|x\right|+c
\frac{x^2}{2}
\frac{x^2}{2}+c
14
What is the derivative of ln(x^2)
x2 ln
x2 /2
2/x
xln2
15
What is the Quotient Rule?
{u’v - uv’} / {v^2}
u’v + uv’
uv’ + vu’
16
What is the derivative of \cos^{-1}\left(x\right)
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1+x^2}}
\frac{1}{x^2+1}
17
What does the intermediate Value Theorem guarantee?
The area under the curve is finite
A max or min exists
A value between f(a) and f(b) is achieved
The derivative exists
18
What is the derivative of e
x
?
blnx
xlnb
ex
1/ex
19
What function has the derivative\frac{1}{1+x^2}
sec-1 x
-csc-1 x
sin-1 x
tan-1 x
20
What does the Mean Value Theorem state?
A function has a local max or min
The limit of the function is continuous
The average value exists
f’(c) = {f(b) - f(a)} / {b - a} for some c
