Khan Academy: Analyzing Mistakes When Finding Extrema (Example 2)

Analyzing the work of someone who tried to find extrema of a function, to see whether they made mistakes.

Learn how the second derivative of a function is used in order to find the function's inflection points. Learn which common mistakes to avoid in the process.

See worked example of how to find the appropriate expression to use in order to solve word problems using definite integrals.

Finding the rate of change of an angle that a falling ladder forms with the ground.

Sal finds the intervals where g(x)=-x^4+6x^2-2x-3 is concave down/up by finding where its second derivative, g'', is positive/negative.

Finding the appropriate expression to use when looking for the total distance traveled over a certain time interval.

Finding the appropriate expression to use when looking for the position at a certain time.

Taking the derivative of f(x)=x^3-12x+2 and graphing the derivative, so we can tell when f is increasing or decreasing, and where is its relative extremum points.

When we have a related rates problem on our hands, it's best to first make sure we understand all the involved quantities.

Given a motion problem, find the expression that can be used in order to solve the problem.