Concave Up
Definition
Concave up refers to the shape of a graph where it curves upward, resembling a smiley face. It indicates that the second derivative of a function is positive.
Analogy
Imagine a roller coaster track that starts at ground level and gradually goes uphill. The track forms an upward curve, just like a concave up graph.
Related terms
Inflection Point: An inflection point is a point on the graph where the concavity changes from concave up to concave down or vice versa.
Increasing Function: An increasing function is one in which the y-values increase as x-values increase.
Second Derivative Test: The second derivative test is used to determine whether a critical point on a graph corresponds to a local maximum or minimum by examining the sign of the second derivative.
"Concave Up" appears in:
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Practice Questions (3)
A particle is moving on the xy-plane starting at t = 0. Its motion can be described by the parametric functions y(t) = 3t^3 - 2t and x(t) = ln(t). At what time, t, is the path of the particle neither concave up nor concave down?
The path of a lost cow on the xy-plane is given in parametric equations by x(t) = t^2 + t and y(t) = t^2-t. Is the path of the cow concave up or down at t=0?
A video game character's attack and defense increase over time (t > 0) is given by the parametric equations A(t) = 3t^2+5t and D(t) = 2t^2+8t. James the gamer plots these values on a plot with attack as the x-axis and defense as the y-axis. Is the resulting curve concave up or concave down?
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