Derivative and Tangent Lines Flashcards
1
Q
Piecewise Functions
- Make sure _ (LHL=RHL for f(x)) to check if there is a point
- If not, then _
- Rewrite f(x) as a _
- Make sure to take out equal to
- Check if LHL=RHL for _
- If they are equal, then write in limit for f’(x)
- If they are not equal then _
A
Continuous, dne, derivative, f’(x), dne
2
Q
x^2 - 9= + or – 3
A
-3 < x < 3
3
Q
Implicit Differentiation
- Find derivative of _ values
- # xa then #ax^(a-1)
- Find derivative of _ values
- # ya then #ay^(a-1)(dy/dx)
- Factor out (dy/dx)
- Divide
- If it equals _ you probably forgot a rule
A
X, y, 0
4
Q
(dy/dx) means the derivative of _ in terms of _.
A
Y, x
5
Q
Always do product rule
A
Xy
6
Q
Always do quotient rule
A
X/y
7
Q
Always do chain rule
A
(X)^#
8
Q
Always do function rule [cos(y)]
A
–sin(y)(dy/dx)
9
Q
sqt(x + y) does not equal sqt(x) + sqt(y)
A
Tip
10
Q
sqt(xy) does equal sqt(x) sqt(y)
A
Tip
11
Q
Higher Order Derivatives
- (d^2y/dx^2)
- y’’
- f’’(x)
- f^2(x)
A
Take the derivative of the derivative
12
Q
F’’(n) means plug in n at very _ and solve.
A
End
13
Q
Equation of a Tangent Line if it is a Possible Point
- Take derivative of the equation
- Plug in x into _ not y’
- Plug in to (y-y1)=m(x-x1)
- _ =m
A
y, derivative
14
Q
Equation of a Tangent Line if it is not a Possible Point
- Make y’ equal to _
- Plug in y
- Solve for x
- Plug in to y’ to get the _
- Plug in slope into tangent equation
- Normal means perpendicular (opposite reciprocal slope)
- Always put _ equations
A
(y-y1)/(y-y2), slope, both
15
Q
When range is not given [0, 2] then put _.
A
x+-2n
16
Q
Make sure to distribute a _.
A
Negative
17
Q
Sqt(x)
A
+-x
18
Q
Linear Approximation
- Choose a number near _
- Find _ of equation and plug in the approximation for the slope
- Plug in to (y-y1)=m(x-x1)
- Plug in real number into the equation of the line
A
X, derivative
