# First And Second Derivative Graphs If the second derivative is negative at a point the graph is concave down.

## First and second derivative graphs If the second derivative is positive at a critical point then the critical point is a local minimum.

First and second derivative graphs. The second derivative tells us a lot about the qualitative behaviour of the graph. Positive intervals on the sign graph. In the applet you see graphs of three functions. On the graph of a function the second derivative corresponds to the curvature or concavity of the graph.

That sign graph because it s a second derivative sign graph bears exactly well almost exactly the same relationship to the graph of. Try to figure out which function is which color. Find the first derivative any stationary points and the sign of f x to find intervals where f increases or decreases. Below the applet click the color names beside each function to make your.

Here are instruction for establishing sign charts number line for the first and second derivatives. To establish a sign chart number lines for f first set f equal to zero and then solve for x. As a first derivative sign graph bears to the graph of a regular function. Show you where.

Is the first derivative and one is the second derivative. To rectify this situation in today s lecture we are going to formally discuss the information that the ﬁrst. If the second derivative is positive at a point the graph is concave up. The power rule for the first derivative if applied twice will produce the second.

If f x is a polynomial with degree n then f x will be a polynomial of degree n 1and f x will be a polynomial of degree n 2.