Where is the slope zero?
- How to Find Relative Minimum | Sciencing.
- Calculus I - Minimum and Maximum Values.
- Worked example: finding relative extrema (video) | Khan Academy?
The Derivative tells us! Using derivatives we can find the slope of that function:. A derivative basically finds the slope of a function. Take the derivative of the slope the second derivative of the original function :. A slope that gets smaller and goes though 0 means a maximum.
On the graph above I showed the slope before and after, but in practice we do the test at the point where the slope is zero :. We say local maximum or minimum when there may be higher or lower points elsewhere but not nearby. If you've found an issue with this question, please let us know.
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Email address: Your name:. Example Question : Intervals. Given Find the -coordinate of the relative maximum on the interval.
How to Find the Minimum or Maximum in a Quadratic Equation
Possible Answers: Cannot be determined. Correct answer:. Explanation : To find relative maximums, we need to find where our first derivative changes sign. Report an Error. Possible Answers:. Determine the relative maxima for the function:.
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Explanation : To determine the relative maxima for the function, we must determine where the first derivative of the function changes from positive to negative. Points of inflection A point of the graph of a function at which it crosses its tangent, and concavity changes from up to down or vice versa is called the point of inflection.
Applications of differentiation - the graph of a function and its derivatives. Extreme points, local or relative maximum and local minimum.
Relative Maxima and Minima - Concept - Calculus Video by Brightstorm
The first derivative test. The second derivative test and concavity.
Finding and classifying critical or stationary points. Finding extreme points. Points of inflection. Finding points of inflection.