Question

You are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x^4 - 2x^3-25x^2+26x+120. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0). (10 points)

Answer 1

To find where P(x)=0, solve the equation. This is because, the solutions of an equation are where the graph touches the x-axis.

To analyze the end behavior of the graph, look at the leading term. Is its coefficient negative or positive?

It is positive so that means that as x approaches +∞, the graph it's self does too.

If you want to find the end behavior of the OTHER side (as x approaches -∞), then look at the exponent of the leading term.

Is it even or odd? Since it is even, the graph itself, f(x), will go the same way that it goes when x approaches positive infinity.

Best of luck!