# Calculus (final question I promise)

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1. Use calculus and algebraic methods to do a complete analysis (i.e., intercepts, critical points, intervals of increase and decrease, points of inflection, intervals of concavity, local maximum or minimum points) for each of the following functions and then sketch the graph of the function. You can use graphing software (Geometer’s Sketchpad or Winplot) to verify your analysis and graph. Keep in mind that your analysis is the most important aspect of this question, not the graph.

ƒ(x) = −x2 + 4x − 3
g(x) = x3 − 6x2 + 9x
h(x) = x4 − 6x2
p(x) = x4 − 4x3

2. In this question, you should determine the asymptotes and then continue with rest of the analysis.

q(x)= -2/(x+3)^2

• Calculus (final question I promise) - ,

After all the help you have received here, you should be able to most of these questions yourself. You should also make the effort to type a ^ before exponents. Show your work and someone will help you.

Factor the equations to find the x-axis interecepts. plug in x = 0 to get the y axis intercepts. Take the first derivatives and set it equal to zero to find the critical points. Take the second derivatives at critical points to determine concavity intervals. You will have to do your own graphs.

• Calculus (final question I promise) - ,

Do you have a graphing calculator in your possession. Just curious.

• Calculus (final question I promise) - ,