Derivative and Tangent Lines Flashcards Preview

AP Calculus AB > Derivative and Tangent Lines > Flashcards

Flashcards in Derivative and Tangent Lines Deck (18):
1

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 _

Continuous, dne, derivative, f’(x), dne

2

x^2 - 9= + or – 3

-3 < x < 3

3

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

X, y, 0

4

(dy/dx) means the derivative of _ in terms of _.

Y, x

5

Always do product rule

Xy

6

Always do quotient rule

X/y

7

Always do chain rule

(X)^#

8

Always do function rule [cos(y)]

–sin(y)(dy/dx)

9

sqt(x + y) does not equal sqt(x) + sqt(y)

Tip

10

sqt(xy) does equal sqt(x) sqt(y)

Tip

11

Higher Order Derivatives
-(d^2y/dx^2)
-y’’
-f’’(x)
-f^2(x)

Take the derivative of the derivative

12

F’’(n) means plug in n at very _ and solve.

End

13

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

y, derivative

14

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

(y-y1)/(y-y2), slope, both

15

When range is not given [0, 2] then put _.

x+-2n

16

Make sure to distribute a _.

Negative

17

Sqt(x)

+-x

18

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

X, derivative