The mean value theorem applies to g(x) on [a,b] when...

g(x) is continuous on [a,b], and differentiable on (a,b).

X(t) describes the motion of a particle on the x axis. The particle is slowing down when...

X'(t) and X''(t) have different sign.

The instantaneous rate of change of g(x) at point c., The slope of the tangent line to g(x) at x = c.

c is a critical number of h(x) if...

h(x) is defined and h'(x) is not., h(x) is defined and h'(x) = 0.

If c is a critical #, according to the first derivative test, h(c) is a relative minimum if...

h'(c) changes from negative to positive at x = c.

m(x) has an inflection point whenever...

m''(x) changes sign and m(x) is continuous.

studbud

AP Calculus AB Derivatives

10 termsStudBud Administration35 plays

Simple Derivative application review.

Flashcards10 cardsFPractice quizPHost liveL

Questions 10

Answers

1
The mean value theorem applies to g(x) on [a,b] when...
g(x) is differentiable on (a,b)
g(x) is continuous on [a,b]
g'(c) = [g(b) - g(a)]/(b - a) for some c on (a,b).
g(x) is continuous on [a,b], and differentiable on (a,b).
2
X(t) describes the motion of a particle on the x axis. The particle is slowing down when...
X'(t) and X''(t) have different sign.
X'(t) and X''(t) have the same sign.
X(t) gets tired.
X(t) and X'(t) have different sign.
3
g'(c) is ....
Math gibberish I don't understand.
The instantaneous rate of change of g(x) at point c.
The average rate of change of g(x) on an interval [a,b]
The slope of the tangent line to g(x) at x = c.
4
c is a critical number of h(x) if...
h(x) is defined and h'(x) is not.
h(x) is undefined.
h(x) is defined and h'(x) = 0.
h'(x) is undefined.
5
X(t) describes the motion of a particle on the x axis. The particle is at rest whenever...
X'(t) = 0
X(t) is on vacation.
X''(t) = 0
X(t) = 0
6
If c is a critical #, according to the first derivative test, h(c) is a relative minimum if...
h'(c) changes from negative to positive at x = c.
h'(c) changes from positive to negative at x = c.
h'(c) = 0
h'(c) in undefined
7
According to the second derivative test, h(c) is relative minimum if...
h''(c) is undefined
h''(c) < 0
h''(c) > 0
h''(c) = 0
8
m(x) has an inflection point whenever...
m''(x) changes sign and m(x) is continuous.
m(x) works out at the gym.
m''(x) changes sign.
m'(x) changes sign.
9
Concavity depends on ...
The second derivative
The discriminant
The first derivative
The second diminutive
10
c is not a critical number of h(x) if...
h(x) discontinuous at x = c.
h(c) is undefined.
h(x) has a cusp at x = c.
h'(x) has a vertical asymptote at x = c.

AP Calculus AB Derivatives Flashcards | StudBud