In the same way that critical points indicate where a function changes direction, inflection points indicate where a function changes concavity. If a function is concave down (curving downwards like a rainbow) and hits an inflection point, it'll become concave up (curving upwards like a bowl). Conversely, if a function is concave up and hits an inflection point, it'll become concave down.

Once you find the critical points of a function, you can use the first derivative test to say where the function is increasing and where it's decreasing. This will also allow you to draw conclusions about the local extrema of the function at each of the critical points.

The critical points of a function are the points where the function changes direction. If the function was increasing and reaches a critical point, it starts decreasing there. Conversely, if a function was decreasing and reaches a critical point, then it starts increasing there. Therefore, the critical points of a function are the points that represent local maxima and minima of the function (its extrema). To find critical points, Take the derivative of the function and set the derivative equal to 0 Find the values of x that make the derivative equal to 0, or make it undefined. These are the critical numbers. Use the first derivative test to see whether or not the function actually changes direction at the critical numbers. Verify that the critical numbers are in the domain of the function. If a critical number is in the domain of the function and the first derivative test tells you that the function changes direction at the critical number, then the critical number is in fact a critical point of the function, and it therefore represents at least a local maxima or local minima of the function. Depending on the function's value everywhere else, the critical point may also be the function's absolute maximum or absolute minimum.

We're often asked to use linear approximation to estimate the root of a constant. To do this, we just need to compare the given value to a function that's similar.

The linear approximation of a function at a point is just the equation of the tangent line there. Since the value of the tangent line is very close to the value of the function near the point of tangency, we can use the linear approximation to estimate the function's value near that point.

A company can use the sales decline formula to calculate how fast revenue will decline.

Compounding interest on an amount continuously makes the amount grow faster.

The half-life of an element is the amount of time it takes for that element to decay to half of its original amount.

The average rate of change of a function over an interval is the average slope of the function over the same interval.