Engineering Board Exam Reviewer · Curve Analysis: Critical Points, Concavity, and Inflection · hard

How many inflection points does f(x)=x5-5x4 have?

1. 2
2. 1
3. 0
4. 3

Answer

B. 1

Solution

f''(x)=20x3-60x2=20x2(x-3). The zero at x=0 is a double root, so f'' does not change sign there. Only x=3 is an inflection point.

More Curve Analysis: Critical Points, Concavity, and Inflection questions

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

All Curve Analysis: Critical Points, Concavity, and Inflection questions