Derivative Quiz

Example Questions From the Test

• 2For f(x) = x⁴ − 4x², what does the second derivative reveal about the graph at x = 0?
  • The graph is concave up there because f″(0) = 8.
  • The graph is concave down there because f″(0) = −8.
  • The graph has zero concavity there because f″(0) = 0.
  • Concavity cannot be assessed there because f′(0) = 0.
• 8Use the linear approximation of f(x) = √x at x = 4 to estimate √4.1.
  • 0125, using a slope of 1/8 at x = 4
  • 05, using a slope of 1/2 at x = 4
  • 025, using L(x) = 2 + (1/4)(x − 4)
  • 1, adding the entire input change directly to √4
• 10Which values are the critical numbers of f(x) = x³ − 3x?
  • x = 0 only, because the cubic term vanishes there
  • x = 1 only, because only the positive square root is considered
  • x = −1 and x = 1, because f′(x) = 3x² − 3 equals zero at both
  • x = −3 and x = 3, because the coefficient of x is −3