Second Derivatives Of Logarithmic Functions worksheets
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Q. Over what interval(s) is f(x) decreasing?
answer choices
(-3, 1)
(-∞, -5) ∪ (0, 2)
(-∞, -3) ∪ (1, ∞)
(-5, 0) ∪ (2, ∞)
Q. If (a,b) is a local maximum, then what will be true about f''(a)?
answer choices
It's positive
It's negative
It's zero
Cannot be determined
Q. If (a,b) is a local minimum, then what will be true about f''(a)?
answer choices
It's postive
It's negative
It's zero
Cannot be determined
Q. The concavity of a function is described by its _______________.
answer choices
first derivative
second derivative
third derivative
expression
Q. The slope of a function is described by its ____________.
answer choices
first derivative
second derivative
third derivative
expression
Q. For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.
answer choices
increasing
decreasing
concave up
concave down
Q. Over what intervals is f(x) decreasing?
answer choices
(-∞, -1) ∪ (1, ∞)
(-∞, -√3) ∪ (0, √3)
(-1, 1)
(-√3, 0) ∪ (√3, ∞)
Q. If a function's FIRST derivative is negative at a certain point, what does that tell you?
answer choices
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
Q. Use the sign chart for f'(x).
There is(are) ...
There is(are) ...
answer choices
a local maximum at x = -2.
a local maximum at x = 4.
local maxima at x = -2 and x = 4.
no extrema.
Q. Use the sign chart for f'(x). There is(are) ...
answer choices
a local maximum at x = -2.
a local minimum at
x = -2 and a local maximum at x = 4.
x = -2 and a local maximum at x = 4.
a local maximum at
x = -2 and a local minimum at x = 4.
x = -2 and a local minimum at x = 4.
no extrema.
Q. Find the second derivative of the function:
f (x) = 2x - 5x6
f (x) = 2x - 5x6
answer choices
f ''(x)= 2 - 30x
f ''(x) = 2-30x5
f ''(x) = -30x5
f ''(x) = -150x4
Q. Identify the critical points of the following function:
g(x)=2x3-3x2
g(x)=2x3-3x2
answer choices
x=-1,1
x=0,0
x=0,-1
x=0,1
Q. How many extrema are in the picture?
answer choices
2
3
4
5
Q. If f '(3) = 0 and f"(3) < 0, then which of the following must be true?
answer choices
There is a local max at x=3
There is a local min at x = 3
There is an inflection point at x = 3
There is an x-intercept at x = 3
Q. On what interval(s) is the function
y = x^3 + 6x^2
concave down?
y = x^3 + 6x^2
concave down?
answer choices
(-∞,-4)
(-∞,-2)
(-2,∞)
(0,∞)
Q. Where is the point of infection for the function y = x^3 + 6x^2?
answer choices
0
-4
-2
4
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