f(x)=x^6-10*x^5-7*x^4+80*x^3+12*x^2-192*x
how to find the answer an its graph???
y = x^6-10x^5-7x^4+80x^3+12x^2-192x
= x(x^5-10x^4-7x^3+80x^2+12x-192)
you know any rational roots will be factors of 192. There appear to be none except x=0.
If you visit wolframalpha.com and enter the formula, you will find one root near x=10, but that is the only real nonzero root.
To see what happens near x=0, try visiting
http://rechneronline.de/function-graphs/
set the x range -10 to 10
y -1000 to 1000
To find the answer to the given function, f(x) = x^6 - 10x^5 - 7x^4 + 80x^3 + 12x^2 - 192x, we can follow these steps:
1. Determine where the function intersects the x-axis: To find the x-intercepts, set f(x) equal to zero and solve for x. In this case, we have to solve the equation x^6 - 10x^5 - 7x^4 + 80x^3 + 12x^2 - 192x = 0.
2. Find the critical points: These are the points where the function has a maximum, minimum, or an inflection point. To find the critical points, calculate the derivative of the function and find where it equals zero.
3. Determine the concavity: To identify where the function is concave up or concave down, find the second derivative of the function and determine its sign.
4. Sketch the graph: With the information obtained from the previous steps, plot the x-intercepts, critical points, and use the concavity information to determine the behavior of the function between those points.
If you're looking to visualize the graph, you can use a graphing calculator or a computational software like Wolfram Alpha, Desmos, or MATLAB. These tools will help you plot the graph accurately based on the equation provided.