The MVT, Mean Value Theorem,

applies to only differentiable functions

The IVT, Intermediate Value Theorem,

applies to all continuous functions

All continuous functions are differentiable.

Evaluates limits of the form "0/0"

What are the three parts to continuous?

limit exists, point exists, and they're equal

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Calculus Topics

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Answers

1
A differentiable function with a local minimum at x=c will have:
f ' (c) = 0 and f " (c) < 0
f ' (c) = 0 and f " (c) = 0
f " (c) = 0 and f ' (c) > 0
f ' (c) = 0 and f " (c) > 0
2
The MVT, Mean Value Theorem,
what is that?!?!? MVT?
applies to all functions
applies to continuous functions
applies to only differentiable functions
3
The only derivative equal to itself is the exponential function y = e^x
False
True
4
\int_{ }^{ }(2x+3)dx
x2 + 3x + C
2
x2 + C
2x + 3 + C
5
What is the derivative of h(x)=g(x)f(x)
f ' (x) g ' (x)
f (x) f ' (x) + g (x) g ' (x)
g ( f ( x ) ) f ' (x)
f ' (x) g (x) + f (x) g ' (x)
6
The IVT, Intermediate Value Theorem,
applies to all functions
what is that?!?!? IVT?
applies to all continuous functions
applies to only differentiable functions
7
Which is false?
If a function is concave down then f " (x) < 0.
Critical values are when f '( x)=0 or DNE
All continuous functions are differentiable.
All differentiable functions are continuous.
8
\frac{d}{dx}(\sin^{^{-1}}x)=
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{\sqrt{x^2-1}}
\frac{1}{\sqrt{x^2-1}}
\frac{1}{x^2+1}
9
L'Hopital's Rule
is a derivative
Evaluates limits of the form "0/0"
Is the quotient rule
evaluates and applies to all limits
10
A graph f(x) with all x-values such that f '(x)<0 and f "(x)>0 is...
decreasing and concave down
increasing and concave up
increasing and concave down
decreasing and concave up
11
\int_{ }^{ }\ln xdx
ex + C
x lnx + x + C
xlnx - x + C
\frac{1}{x}+C
12
What two things do you need for the EQUATION of the TANGENT LINE?
An x value and a y value
two points
Point and Slope
derivatives and integrals
13
What are the three parts to continuous?
the limit exists and the point exists but they may not be equal
must be differentiable
limit exists, point exists and differentiable
limit exists, point exists, and they're equal
14
f '(x) = sec²x , f(x)=
tan x
2 secx tanx
tan x + C
tan2x
15
If y=g(f(x)) , then y'=
g ' (x) f( x) f ' (x)
g ' ( f(x) ) f ' (x)
g ' ( f (x) ) + f ' (x)
g ' (x) f(x) + g(x) f ' (x)
16
What is the answer using test taking strategies?
5x + 3x2
5x - 3x2
3x - 5x2
- 5x - 3x2

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