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Course: Staging content lifeboat > Unit 4

Lesson 1: Hidden Tutorial for Skill Checks (all Math: Calculus)
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Staging content lifeboat
Hidden Topic for Skill Checks (all Math: Calculus)
Hidden Tutorial for Skill Checks (all Math: Calculus)
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Test Yourself: First order differential equations

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Problem

An unknown function f solves the differential equation
f′(x)=−f(x)+x−1
and satisfies the condition f(2)=1.
Use the information above to complete the statements below.
f′(2)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
f′(2) is
f″(2)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
f″(2) is
At the point 2, the function f