Business Calculus
- What is one purpose of the first derivative in evaluating functions? Explain
- What is the definition of a Critical Number?
- Define local and extrema ( Local Maximum and Minimum) explain and provide a picture if necessary.
- For functionf(x)=−x3−4x+8f(x)=−x3−4x+8,find the derivative and the intervals for which function is increasing or decreasing.
- What is the second derivative? Write the formula and the appropriate notation
- What is the definition of concavity? Draw appropriate pictures.
- What is the definition of an inflection point?
- Find the inflection points f(x)=ln(x2−4x+5)f(x)=ln(x2−4x+5). SHow all of your work and explain.
- Define Absolute Maximum and Absolute Minimum
- State Theorem 1 ( extreme value theorem)
- State Theorem 2 and list all 5 steps
- State Theorem 3 ( Second Derivative test)
- Find the local Maximum and minimum values of f(x)=x3−6x2f(x)=x3−6x2on interval [-1,7]
- List the steps for optimization ( they’re 4)
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