First Derivative Test in Calculus
Authored by Lisa Lee
Mathematics
11th - 12th Grade
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25 questions
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1.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
If a function's FIRST derivative is negative at a certain point, what does that tell you?
The function is increasing at that point
The function is decreasing at that point
The concavity of the function is up at that point
The concavity of the function is down at that point
2.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.
increasing
decreasing
concave up
concave down
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If (a,b) is a local minimum, then what will be true about f'(a)?
It's positive
It's negative
It's zero
Cannot be determined
4.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Over what intervals is f(x) decreasing?
(-∞, -1) ∪ (1, ∞)
(-∞, -√3) ∪ (0, √3)
(-1, 1)
(-√3, 0) ∪ (√3, ∞)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The concavity of a function is described by its _______________.
first derivative
second derivative
third derivative
expression
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The slope of a function is described by its ____________.
first derivative
second derivative
third derivative
expression
7.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.
increasing
decreasing
concave up
concave down
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