Which formula is the alternate definition of derivative at a point?

\frac{f\left(x\right)-f\left(a\right)}{x-a}

What does the Mean Value Theorem guarantee?

A point where slope = average rate of change

What is the average value of a function f on[a,b]?

\frac{1}{b-a}\int_a^bf\left(x\right)dx

What does the Intermediate Value Theorem state?

The function takes every y-value between f(a) and f(b)

What theorem allows you to evaluate \int_a^bf\left(x\right)dx=F\left(b\right)-F\left(a\right)?

Fundamental Theorem of Calculus, Part 2

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Quiz AB

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Questions 20

Answers

1
The Chain Rule is used when differentiating?
A logarithmic function
A product of functions
A quotient of functions
A composition of functions
2
Ifv\left(t\right)is velocity andx\left(8\right)=4, how do you find x\left(2\right)?
None of the above
\int_8^2v\left(t\right)dt+4
x\left(2\right)=\int_0^2v\left(t\right)dt
x\left(2\right)=x\left(8\right)-v\left(2\right)
3
What rule is used to differentiate u\left(x\right)v\left(x\right)?
Power Rule
Quotient Rule
Product Rule
Chain Rule
4
What does the Extreme Value Theorem state?
f is always continuous
A max or min exists on [a,b]
The average rate of change is 0
f is differentiable
5
Which formula is the alternate definition of derivative at a point?
\frac{f\left(x\right)-f\left(a\right)}{x-a}
\frac{f\left(x+h\right)-f\left(x\right)}{h}
\frac{f\left(a+h\right)-f\left(a\right)}{h}
\frac{dy}{dx}
6
What is the derivative of e^x?
x^e
\ln x
e^x
e^{x+1}
7
If f\left(a\right)=b and g is the inverse of f, what is g'\left(b\right)
f'\left(a\right)
\frac{1}{f'\left(a\right)}
g\left(a\right)
f'\left(b\right)
8
What is the derivative of \sin x?
-\cos x
-\sin x
\sec x
\cos x
9
What does the Mean Value Theorem guarantee?
A point where slope = average rate of change
Instantaneous rate is constant
F is invertible
A max and min on an interval
10
What is the derivative of secx?
\sec^2x
\tan x
\csc x
\sec x\tan x
11
What is the power rule for differentiation?
\frac{d}{dx}x^n=nx
\frac{d}{dx}x^n=\ln x
\frac{d}{dx}x^n=x^n\ln x
\frac{d}{dx}x^n=nx^{n-1}
12
What is the derivative of \cot x?
\tan x
\sec^2x
\csc x\cot x
-\csc^2x
13
What is \lim_{x\to0}\frac{\sin x}{x}?
0
DNE
∞
1
14
What is \frac{d}{dx}\ln x?
\frac{1}{x}
\ln|x|
xlnx
lnx
15
What is the derivative of \tan x?
\sec^2x
-\tan x
\csc^2x
\cot x
16
If y=a^x, then \frac{dy}{dx}=?
a^x\ln a
\ln x
\frac{1}{x}
a^x
17
What is the average value of a function f on[a,b]?
\frac{1}{b-a}\int_a^bf\left(x\right)dx
f\left(b\right)-f\left(a\right)
\int_a^bf\left(x\right)dx
\frac{f\left(a\right)+f\left(b\right)}{2}
18
What is the derivative of cos^-1x?
\frac{x}{\sqrt{1-x^2}}
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\sqrt{1-x^2}
19
What does the Intermediate Value Theorem state?
A function has an inverse
The Function is constant
The function takes every y-value between f(a) and f(b)
Derivatives exist on close intervals
20
What theorem allows you to evaluate \int_a^bf\left(x\right)dx=F\left(b\right)-F\left(a\right)?
Fundamental Theorem of Calculus, Part 2
Chain Rule
Fundamental Theorem of Calculus, Part 1
Mean Value Theorem

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