Mins/Maxs
Second Derivative
Linearization
Graphs of f, f' and f"
Random
100
The definition of a critical point
Is a point where the derivative is zero or doesn't exist
100
The point on the graph of a function of which the concavity changes from concave up to concave down or concave down to concave up.
A point of inflection
100
Find the linearization of f(x)=x^4 at x=1.
L(x)=4x-3
100
How many points of inflection does this graph have?3
100
If f' is increasing, then f" is..
Positive
200
What the first derivative test finds.
Relative maximums and minimums
200
When the second derivative is positive, the first derivative is______
Increasing
200
Find the linearization of f(x) = 1/x at x=2.
L(x)=-1/4 x +1
200
If this is the graph of f', where is f concave up?(-infinity, -3) (-1, 2) and (4, infinity)
200
If f is concave down, then f' is....
Decreasing
300
Find the relative min of (x+2)^2 - 4
(-2,-4)
300
Determine the interval(s) where y=x^3+3x^2+6 is concave up.
(-1, infinity)
300
Find the linearization of f(x)=(sinx)^2 at x = pi/4.
L(x)=x + (2-pi)/4
300
If this is the graph of f', then where does f have relative maximum?What is at x=-2, and x = 3?
300
Find the c value guaranteed by the Mean Value Theorem for f(x) = x^2-3x on the interval [1, 4].
x=2.5
400
Why is (0 , 0) not an Extrema of the function f(x) = x^4 - 4x^3.
f' does not change sign at 0.
400
Find the equation of the tangent line to the graph of y=x^3+6x^2 at its Point of Inflection.
y=-12(x+2)+16
400
Find the linearization of y=e^sqrt(x) at x=1.
L(x)= e/2 x + e/2
400
If this is the graph of f', where are the Points of Inflection of f?x=-3 x=-1, x=2, x=4
400
Let f(x) be a polynomial function such that f(3)=5, f'(3)=0, and f "(3)=-2. The point (3, 5) is a ________________________ of the graph of f. (Be specific.)
A relative maximum
500
Use the linearization of y=x^3 at x=1 to approximate the value of 1.02 ^ 3.
1.02^3 is approximately 1.06.