Concave Down

AP Pre-Calculus

AP Calculus AB/BC - 4.6 Approximating Values of a Function Using Local Linearity and Linearization

AP Calculus AB/BC - 5.3 Determining Intervals on Which a Function is Increasing or Decreasing

AP Calculus AB/BC - 5.6 Determining Concavity

AP Calculus AB/BC - 5.9 Connecting a Function, Its First Derivative, and its Second Derivative

How does the tangent line approximation change when the function is concave down?

Which of the following pairs of parametric equations are concave down at t = 1?

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?

A particle moves on the xy-plane. Its motion can be described by the parametric functions y(t) = sin(t) and x(t) = cos(t). For which t in the interval 0 ≤ t < 2π is the path of the particle concave down?

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?