Physics I / Integrated single-variable calculus problems
Practice question · Fill in the blanks

Complete the statement with the correct term.

The inflection point of f(x)=x33xf(x) = x^{3} - 3x is found by solving f''(x) = ______.

Word bank: D · n · k · 0

Hints
  1. The term describes the second derivative changing sign.
  2. A vanishing second derivative is not enough, the sign must actually flip.
Show the answer

The inflection point of f(x)=x33xf(x) = x^{3} - 3x is found by solving f''(x) = 0.

Why

f(x)=6xf''(x) = 6x. Setting 6x=06x = 0 gives x=0x = 0. Concavity changes sign there: f<0f'' < 0 for x<0x < 0, f>0f'' > 0 for x>0x > 0.

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