Term
What is an extrema?
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Definition
The only local maximum, or the only local minimum
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Term
How do you do a first derivative test (find the behavior of a function analytically without plotting it)?
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Definition
1.) Take the Derivative of the Function
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2.) Set the Derivative Function to Equal Zero and solve it for "x" (If the derivative of the function can never equal zero, then there are no critical points: if this is the case then use a value that would make the function undefined and use it as if it was a critical point)
2a.) Factor it further to where you have multiple values of "x"
or
2b.) Use the Quadratic Formula to Obtain Multiple Values For "x"
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3.) Use the multiple values of "x" you have found, and set a test value between -infinity and your first value, your first value and your second value, and your second value and positive infinity. Represent this information as a chart.
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4.) Substitute your test values into the derivative in place of "x" and mark whether the solution to each value is positive or negative and whether the function is increasing or decreasing on your chart
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5.) Your x-values are the critical points, mark whether they are maximums or minimums depending on whether or not the slope right before the function is positive or negative
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Term
What number of critical points does this function have?
f(x)=((x+A)/(x+B))
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Definition
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Term
What is the Derivative of...
(sqrt(x^2+A))
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Definition
x/(sqrt(x^2+A))
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Term
What are the Critical Points of this function?
(sqrt(x^2+A))
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Definition
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Term
When looking at a graph, how do you find the critical points of a function?
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Definition
Wherever the function crosses the x-axis is a critical point. The critical point is the x-value of the x-intercept
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