Sketch a continuous function f on some interval that has the properties described. Answers will vary.


The function f satisfies f'(-2) = 2, f'(0) = 0, f'(1) = -3 and f'(4) = 1.

Verified step by step guidance

1. Understand that f'(x) represents the derivative of the function f(x), which gives the slope of the tangent line to the curve at any point x. The given values of f' indicate the slope of the tangent line at specific points.
2. At x = -2, f'(-2) = 2, which means the slope of the tangent line at this point is 2. This suggests that the function is increasing at x = -2.
3. At x = 0, f'(0) = 0, indicating that the tangent line is horizontal at this point. This could be a local maximum, minimum, or a point of inflection.
4. At x = 1, f'(1) = -3, meaning the slope of the tangent line is -3, so the function is decreasing at this point.
5. At x = 4, f'(4) = 1, which implies the slope of the tangent line is 1, indicating that the function is increasing at this point.