Area 51
This is given by the "signed" area under the curve
What is the definite integral?
This is a function whose derivative equals f
What is an antiderivative of f?
To find maximums and minimums, we find these by setting f'(x)=0 and finding when f' is not defined
What are critical points?
This is what a function is doing when f'(x)>0
What is increasing?
When this happens, then the tangent line to the graph at the given point is horizontal
What is f'(x)=0?
This is the mathematical notation used to write long sums in short form
What is the Sigma notation?
The most general antiderivative of 2x
What is x^2+C?
This is the process that needs to be done when trying to find two numbers with a given product and minimal sum
What is optimization?
What is the second derivative?
This is what the Mean Value Theorem says that the derivative must equal at some point
What is the slope of the secant line between (a,f(a)) and (b,f(b))?
This is the type of estimate for x^2 when using any number of intervals but always using the right endpoints in [0,100]
What is an overestimate?
The most general antiderivative of 1/(1+x^2)
What is arctan(x)+C?
These are two common math facts used when doing optimization.
What is related triangles and the pythagorean theorem?
This is the conclusion of a theorem when f'(c)=0 and f''(c)<0
What is the Second Derivative test for a local maximum?
This is a method that relies on the Extreme Value Theorem and consists on finding the critical numbers and comparing their values with the endpoint values
What is the Closed Interval Method?
This is the approximation of f using the right endpoints and 5 intervals
What is R5?
The most general antiderivative of sin(x)
What is -cos(x)+C?
When we plug in "what we have" into the function obtained in "what we want"
What is using the constraint?
The limit of f/g is the same as the limit of f'/g'
What is the conclusion of L'Hospital's Rule?
What are the absolute min and absolute max of |x| on the interval [-3,1]?
It is the name of the expression that we used for either Rn, Ln or Mn
What is a Riemann sum?
The most general antiderivative of e^x
What is e^x+c?
These are the dimensions of a rectangle with maximum area but fixed perimeter
What is a square?
L'Hospital's Rule applies to these two forms
What are 0/0 and ∞/∞?
When sketching a function’s graph, these features are identified by analyzing where the first and second derivative change sign, giving the full picture of the curve’s shape.
What are local maxima, minima, and inflection points?