How Do We Measure Speed?
What is the formula for average velocity and why?
(s(b) - s(a)) / (b - a)
Velocity is calculated by finding the position times the time of the object, so this equation simply finds the change in position over the change in time.
If a function goes up to infinity (or down to negative infinity) around a specific x-value, this is called a ____?
Vertical Asymptote
In terms of "u" and "v", the product rules is defined as...
d/dx (uv) = (u')(v)+(u)(v')
What is the formula for the chain rule?
d/dx f(g(x)) = f'(g(x)) (g'(x))
What is the constant rule?
If f(x)=k, where k is any real number, then f'(x)=0
Using the following table, how fast is the object traveling from 0 to 2 seconds?
T(sec) 0 1 2 3
H(ft) 6 90 142 162
68 ft per second
Determine the end behavior of f(x)=-10x^(4) as x approaches positive infinity and as x approaches negative infinity
f(x) -> -∞ as x -> +∞
f(x) -> -∞ as x -> -∞
What is the derivative of f(m)=(4m^(3)-5)(4m+7)?
64m^(3)+84m^(2)-20
What is the derivative of f(x)=2(4x+3)3?
f'(x)=24(4x+3)2
What is the derivative of f(x)=7x-2
f'(x)=7
What is the instantaneous velocity of a particle on f(t) = t^2 at t = 3 (ft/s) ?
6 ft per second
In the rational function f(x)=x^(2)-4/(x-2), what value of x is the hole located at?
x = 2
What is the derivative of h(t)=(4t^(2)-5)/(2t-1)?
(8t^(2)-8t+10)/(4t^(2)-4t+1)
What is the derivative of f(x) = e3x+4?
e(3x+4)(3)
What is the derivative of f(x)=7x5-1000 ?
f'(x)=35x4
Given the following, what speed is the object traveling at when t = 1 second?
t(sec) 0.9 1 1.1
h(ft) 83.04 90 96.64
68 feet per second
What is wrong with the following statement: the graph of a polynomial of degree 5 cuts the horizontal axis 5 times.
The degree of the polynomial indicates only the possibility of turns. For example, x^5 only crosses the x axis once.
What is the derivative of 7^(x) 2x+5?
(2ln(7)x+5ln(7)+2)7^(x)
What is the derivative of f(x)= 4√ (-3x^(4)-2) ?
-3x3/(-3x4-2)3/4
What is the derivative of f(x)=3x5+3x-5?
f'(x)=15x4+3
lim 20ft/sec
h->0
Given the function f(x)=(x^(2)-9)/(4x^(2)-1), find: the y intercepts, horizontal asymptotes, zeros, and vertical asymptotes.
Y intercept = (0,9), Horizontal Asymptote y = 1/4, Zeros at x = 3 and -3, and Vertical Asymptote at x = 1/2 and -1/2.
What is the derivative of 4ex/x2?
(4x-8)ex/x3
What is the derivative of f(x)=(3x3+1)(-4x2-3)4?
x(4x2+3)3(132x3+27x+32)
What is the derivative of f(x)=2x10-5x3+6x+e?
f'(x)=20x9-15x2+6