A curve passes through the point and satisfies the property that the slope of the tangent at any point is . What is the equation of the curve?

Answer and explanation

Correct answer: B.

  1. Step 1: The slope of the tangent is .
  2. Step 2: Separate variables: . Integrate both sides: .
  3. Step 3: Use the point to find : . The curve is .
Answer
.
Why not the others: corresponds to slope ; is a straight tangent line; corresponds to negative slope .

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