Test 2 Flashcards
Sections 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 4.1, 4.2, 4.3
Product Rule:
f’xgx + g’xfx
Quotient Rule:
(gxf’x - fxg’x) / gx^2
Average Rate of Change:
Finding the slope of the secant line
Instantaneous Rate of Change:
Finding the slope of the tangent line
Speed
The absolute velocity
Finding the Maximum Height in a Problem:
Find the height where velocity is equal to zero.
Higher Derivatives:
Position = fx
Velocity = f’x
Acceleration = f’‘x
Derivative of Sinx
cosx
Derivative of Cosx
-sinx
Derivative of Tanx
sec^2x
Derivative of Secx
secxtanx
Derivative of Cotx
-csc^2(x)
Derivative of Cscx
-cscxcotx
Chain Rule:
f(g(x))’ = f’(g(x))(g’(x))
Implicit Differentiation Solving Steps:
- Differentiate both sides of the equation with respect to x.
- Solve for y’.
- Plug in the point that you need the tangent line of.
Derivative of Lnx:
1/x
Derivative of Ln(f(x)):
f’x/fx
Derivative of B^x
(lnb)b^x
Derivative of Logb(x):
1/(x*ln(b))
Logarithmic Differentiation:
This is helpful when an equation has a product or quotient with several factors.
You take the ln of both sides fo the equation.
Steps to Solving Related Rates:
- Identify variables and the rates they have related.
- Find an equation relating the variables and differentiate it.
- Use given information to solve the problem.
Linear Approximation:
Uses the tangent line to the graph of a function at x=a to approximate f(x) for x near a.
Linearalization Formula:
L(x) = f’(a)(x-a)+f(a)
Critical Point:
Occurs where f’(c) = 0 or DNE.
Mean Value Theorem:
f’(c) = [f(b)-f(a)]/[b-a]
If f’x>0, then f is:
Increasing.
If f’x<0, then f is:
Decreasing.
If f’x changes from + to -, then fx is a:
Local max.
If f’x changes from - to +, then fx is a:
Local min.
