Dustobusto said:Homework Statement
Find the points on the graph of y = x3ex where the tangent line is horizontal.
(Your answer should include x-values and y-values)Homework Equations
Product rule
fg'+gf'The Attempt at a Solution
(x3)(ex)+(ex)(3x2)
x3ex+3x2ex= y'
x3ex+3x2ex= 0
x2ex(x+3) = 0
x = -3
Going back to original equation, and plugging in x:
y = -33e-3
y = -27e-3
y ≈-1.34
Not sure if I did this correctly.
Mark44 said:Looks fine, but you should provide a summary of what you found - something like this: The only point with a horizontal tangent is (-3, -27e-3), or approximately (-3, -1.34).
To find the points on a graph, you will need to locate the x and y coordinates of each point. You can do this by looking at the axes of the graph and finding where the lines intersect. The x coordinate represents the horizontal position and the y coordinate represents the vertical position of the point.
Finding the points on a graph is important because it allows you to accurately interpret and analyze the data presented in the graph. It also helps you understand the relationship between the variables represented on the graph.
There are a few methods for finding points on a graph, depending on the type of graph. For a line graph, you can use the slope-intercept form (y=mx+b) to find the points. For a scatter plot, you can use a trend line or regression equation to find the points. Additionally, you can use the scale and grid lines on the graph to estimate the points.
In most cases, it is not possible to find all the points on a graph. This is because there are an infinite number of points between two given points on a graph. However, you can find a close approximation of the points by using the methods mentioned in question 3.
To check if your points are accurate, you can use them to plot a line or curve on the graph and see if it matches the original data points. You can also use a calculator or software to calculate the values of the data points and compare them to the points on the graph. Additionally, you can use the scale and grid lines on the graph to ensure the points are in the correct location.