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

For what value of k does f(x)=x3+kx2 have an inflection point at x=2?

1. 6
2. -3
3. 12
4. -6

Answer

D. -6

Solution

f''(x)=6x+2k. Setting f''(2)=12+2k=0 gives k=-6.

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