Curve Analysis: Critical Points, Concavity, and Inflection — Engineering Board Exam Practice Questions

10 free engineering board exam reviewer questions on Curve Analysis: Critical Points, Concavity, and Inflection (Differential Calculus), each with the correct answer and a worked solution.

1. Find the absolute minimum value of f(x)=x4-4x3+10.
2. How many inflection points does f(x)=x5-5x4 have?
3. Find the maximum value of f(x)=xe-x for x≥0.
4. For what value of k does f(x)=x3+kx2 have an inflection point at x=2?
5. Find the absolute maximum value of f(x)=x3-3x on the interval [0,2].
6. Determine the intervals of concavity of f(x)=x4-6x2.
7. Find the x-coordinate of the inflection point of f(x)=x3-6x2+9x+1.
8. Find the local maximum value of f(x)=x3-3x2+4.
9. On which interval is f(x)=x2-4x increasing?
10. Find the critical number of f(x)=x2-6x+5.