BC Flashcards

1
Q

Average Rate of Change

A

Slope of secant line between two points, use to estimate instantanous rate of change at a point.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Instantenous Rate of Change

A

Slope of tangent line at a point, value of derivative at a point

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Formal definition of derivative

A

limit as h approaches 0 of [f(a+h)-f(a)]/h

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Alternate definition of derivative

A

limit as x approaches a of [f(x)-f(a)]/(x-a)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

When f ‘(x) is positive, f(x) is

A

increasing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

When f ‘(x) is negative, f(x) is

A

decreasing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

When f ‘(x) changes from negative to positive, f(x) has a

A

relative minimum

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

When f ‘(x) changes fro positive to negative, f(x) has a

A

relative maximum

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

When f ‘(x) is increasing, f(x) is

A

concave up

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

When f ‘(x) is decreasing, f(x) is

A

concave down

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

When f ‘(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a

A

point of inflection

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

When is a function not differentiable

A

corner, cusp, vertical tangent, discontinuity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Product Rule

A

uv’ + vu’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Quotient Rule

A

(uv’-vu’)/v²

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Chain Rule

A

f ‘(g(x)) g’(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

y = x cos(x), state rule used to find derivative

A

product rule

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

y = ln(x)/x², state rule used to find derivative

A

quotient rule

18
Q

absolute value of velocity

A

speed

19
Q

y = sin(x), y’ =

A

y’ = cos(x)

20
Q

y = cos(x), y’ =

A

y’ = -sin(x)

21
Q

y = tan(x), y’ =

A

y’ = sec²(x)

22
Q

y = csc(x), y’ =

A

y’ = -csc(x)cot(x)

23
Q

y = sec(x), y’ =

A

y’ = sec(x)tan(x)

24
Q

y = cot(x), y’ =

A

y’ = -csc²(x)

25
Q

y = sin⁻¹(x), y’ =

A

y’ = 1/√(1 - x²)

26
Q

y = cos⁻¹(x), y’ =

A

y’ = -1/√(1 - x²)

27
Q

y = tan⁻¹(x), y’ =

A

y’ = 1/(1 + x²)

28
Q

y = cot⁻¹(x), y’ =

A

y’ = -1/(1 + x²)

29
Q

y = e^x, y’ =

A

y’ = e^x

30
Q

y = a^x, y’ =

A

y’ = a^x ln(a)

31
Q

y = ln(x), y’ =

A

y’ = 1/x

32
Q

y = log (base a) x, y’ =

A

y’ = 1/(x lna)

33
Q

To find absolute maximum on closed interval [a, b], you must consider…

A

critical points and endpoints

34
Q

mean value theorem

A

if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b)

f ‘(c) = [f(b) - f(a)]/(b - a)

35
Q

If f ‘(x) = 0 and f”(x) > 0,

A

f(x) has a relative minimum

36
Q

If f ‘(x) = 0 and f”(x)

A

f(x) has a relative maximum

37
Q

Linearization

A

use tangent line to approximate values of the function

38
Q

rate

A

derivative

39
Q

left riemann sum

A

use rectangles with left-endpoints to evaluate integral (estimate area)

40
Q

right riemann sum

A

use rectangles with right-endpoints to evaluate integrals (estimate area)

41
Q

trapezoidal rule

A

use trapezoids to evaluate integrals (estimate area)

42
Q

Intermediate Value Theorem

A

If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis.