Chapter 3 Test Flashcards
How do you find the velocity of something at time t?
Take the derivative of the original equation.
How do you find out when something comes to rest?
Set the velocity equation equal to 0.
How do you find the acceleration at time t?
Take the derivative of the velocity equation, or the derivative of the original equation twice.
How do you figure out when an object reaches it’s maximum height?
Set the velocity equation equal to 0.
How do you figure out what an object’s maximum height is?
Plug in the answer from the max height equation (in t) into the original equation.
What is the quadratic formula?
negative b plus or minus the square root of b squared minus 4 a times c divided by 2 a
How do you figure out when an object hits the ground?
Set the original equation equal to 0
How do you find the velocity of an object when it his the ground?
Plug in WHEN it hits the ground to the velocity equation.
How do you figure out how fast something is growing?
Get the derivative of the entire word problem. Even what’s before the equal sign.
If a variable is not present in an equation, what rule should be used?
Constant Rule (don’t take a derivative, just leave as is)
What is the equation used with the ladder word problem?
A^2 + B^2 = C^2
Why can’t you plug in A B and C when taking the derivative of the ladder equation?
Because all of the numbers will then be constants which will make all the numbers 0
What is the equation for the area of a circle?
A = pi R squared
Sum Rule
d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)
Difference Rule
d/dx (f(x) - g(x)) = d/dx f(x) - d/dx g(x)
Constant Multiple Rule
d/dx (c f(x)) = c d/dx f(x)
Constant Rule
d/dx (k) = 0
k is a constant
Power Rule
d/dx x^n = nx^n-1
What is the derivative of x with respect to x?
1
Exponential Rule
d/dx e^x = e^x
Product Rule
d/dx (fg) = f dg/dx + g df/dx
Quotient Rule
d/dx (f/g) = (g df/dx - f dg/dx) / (g^2)
Low Di High minus High Di Low
d/dx sinx
cosx
d/dx cosx
-sinx
d/dx tanx
sec^2x
d/dx cotx
-csc^2x
d/dx secx
secxtanx
d/dx cscx
-cscxcotx
Chain Rule
d/dx [f(x)]^n = n [f(x)] ^n-1 d/dx f(x)
derivative of outer x derivative of inner
How do you find the equation of the tangent line?
- Plug in x to find y OR y to find x
- Take the derivative of the function to find the slope equation
- Plug in x to the slope equation to get the exact value of the slope
- Plug all numbers in to find b
- Rewrite equation correctly
How do you find average velocity?
Average Velocity = Rise / Run
f(y) - f(x) / y - x
Log Rule
d/dx lnx = 1/x
d/dx = ln(f(x)) = 1/f(x) * d/dx f(x) * f’(x)/f(x)
ln(ab)
lna + lnb
ln(a/b)
lna - lnb
What do you do when trying to find implicit differentiation?
Take the derivative of both sides of the equal sign
What rule must be used if ln is outside of a function?
Log Rule
What rule must be used if ln is inside of a function?
Chain Rule
How do you find the linear approximation?
- Find the equation of the tangent line
2. Set equation approximately equal to equation of tangent line
