Extremas
Theorems
Sec/Tan lines
Concavity
Etc.
100
, No extrema
100
What does the extreme value theorem require to apply to an equation?
A continuous function over a closed interval.
100
What is the equation of the secant line from x=0.5 to x=2 using the function .
y=
100
What is the concavity of equation
concave down
100
Does the Extreme Value Theorem apply to function ?
The EVT can not apply to this function because it is not over a closed interval.
200
Max of -2 at x=3
200
What does the mean value theorem require to apply to the function?
The mean value theorem requires to be continuous and differentiable over the same interval.
200
Use the function to find the secant line between x=3 and x=5
y=10(x-3)+15
200
Find the concavity of the equation
Concave Up:
Concave Down:
200
What does the inflection point mean for a function?
An inflection point is where the curve/ concavity switches directions.
300
If , -2 is
Absolute max of 6.350 at x=4
Absolute min of 0 at X=0
300
A car traveled 257 miles, to see Mr. Hawks, in 3 hours. The speed limit of the road is 70mph. The driver was caught speeding. How come?
The MVT proves that the driver was traveling at least 85 mph at one point, so they were speeding.
300
What is the equation of the tangent line of
f(x)=x3+2x2−3x+2 at x=1?
y=4(x-1)-2
300
When is the function increasing and decreasing
Increasing:
Decreasing:
300
What happens to f''(x) on a graph at the inflection point?
The graph of f''(x) would cross over the x-axis and switch signs
400
If f(x)=-2sin(x),
Absolute max of 2 at x=
Absolute min of 0 at x=0
400
What value of c satisfies the mean value theorem for where
c = 9
400
What is the equation of the tangent line of at x=2?
y=3(x-2)+1
400
Find the inflection points of the equation
At (0,0), (2,16)
400
What would f'(x)=0 look like?
This would have a slope of 0, the tangent line would be horizontal.
500
Find the max and min values of
Min of at x=-1
500
What does the Mean Value Theorem prove?
The MVT proves that there is a point that f'(c) is equal to the average rate of change.
500
Find the equation of the tangent line using the formula
y=15(x-5)+10
500
Where is the inflection point for?
At
500
What would f''(x)=3 look like on a graph?
f''(x)=3 would be concave up on a graph.