Differentiating Linear Inequalities vs
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Questions and Answers

When differentiating a linear inequality in two variables, what is the key difference compared to differentiating a linear equation in two variables?

  • The derivative of an inequality is always positive
  • The derivative of an inequality is always negative
  • The inequality sign remains the same when solving for the derivative
  • The inequality sign may change when solving for the derivative (correct)

    • For the linear inequality $2x - 3y > 6$, what is the correct form of the derivative with respect to $x$?

  • $-3$
  • $-\frac{3}{2}$
  • $\frac{3}{2}$
  • $2$ (correct)

    • When differentiating a linear equation in two variables, what is a common misconception?

  • The derivative of a constant term is always $0$ (correct)
  • The derivative will always have the same variables as the original equation
  • The derivative of a linear equation is undefined
  • The derivative will always result in a linear equation

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