Plot the graph of f(x) = x^3 - e^x using a graphing...

Plot the graph of f(x) = x^3 - e^x using a graphing calculator or computer to find all local and global maxima and minima for the following ranges. (a) -1 <= x <= 5 Enter your answers in increasing order to two decimal places. At x = -0.46 , there is a local maximum At x = 0.91 , there is a local minimum At x = 3.73 , there is a global maximum At x = 5 , there is a global minimum At x = , there is a (b) -3 <= x <= 2 Enter your answers in increasing order to two decimal places.

Transcript

00:01 So in this question, we're asked to find the local and global maxima and minima for the function f of x equals x to the third minus e to the x.

00:11 And below, on the left hand side, i plotted some points.

00:15 I plotted negative 1, f of negative 1, and 5 f of 5.

00:21 Because these are the end points of our graph.

00:24 Our domain given is negative 1 is less than or equal to x is less than or equal to 5.

00:30 So in this region, i'm going to plot the endpoints in blue and green respectively, the lower end point and the higher end point.

00:40 Okay, so in this graph, we have some special points.

00:44 We have these endpoints, and we also have some minima, some extrama.

00:48 We have, from left to right, we'll start with this blue point, negative 1, negative 1 .37, let's say.

01:00 This is a local minimum because in a vicinity around this point, depending on your instructor's definition, this is a local minimum because in a neighborhood around this point, it is the lowest point on the interval.

01:17 Because we're only talking about for this interval, x values greater than negative one.

01:25 So by definition, this is the lowest point that it can achieve on that interval, negative 1 to some very small interval around negative 1.

01:36 So that makes it a local extrama and therefore a local minimum because it's the lowest point...

Question

Please give Ace some feedback