Shapeof Graph 2 Math 115 What The Second Derivative Tells Us About

Shapeof Graph 2 Math 115 What The Second Derivative Tells Us About Math 115, what the second derivative tells us about the shape of the graph. recap from the last worksheet: let f (x) be a function (a) c is a critical number of f (x) if f 0 (c) (b) if f 0 (x) > 0 for all x in the interval (a, b), then f is (circle one) increasing or decreasing on (a, b). Section 4.6 : the shape of a graph, part ii. in the previous section we saw how we could use the first derivative of a function to get some information about the graph of a function. in this section we are going to look at the information that the second derivative of a function can give us a about the graph of a function.

Curve Sketching Basics of calculus chapter 4, topic 3—what the second derivative tells usthe second derivative gives us information about the shape of a graph, its co. The second derivative tells you concavity & inflection points of a function’s graph. with the first derivative, it tells us the shape of a graph. the second derivative is the derivative of the first derivative. in physics, the second derivative of position is acceleration (derivative of velocity). The derivative tells us if the original function is increasing or decreasing. because \(f'\) is a function, we can take its derivative. this second derivative also gives us information about our original function \(f\). the second derivative gives us a mathematical way to tell how the graph of a function is curved. Figure 4.5.2: the function f has four critical points: a, b, c,and d. the function f has local maxima at a and d, and a local minimum at b. the function f does not have a local extremum at c. the sign of f ′ changes at all local extrema. using figure 4.5.2, we summarize the main results regarding local extrema.