12.3: Function Analysis of Parametric Equations

Warm up Determine when the function f(x)=arcsin⁡(5𝑥) is increasing and decreasing Determine when the function is concave up and concave down.

The parametric equation x= 𝑡 2 −2𝑡 and y=𝑡+1 is given, Find where the equation is increasing and decreasing, in terms of t. When is the horizontal axis moving to the right? When is the vertical axis moving up? Find where the function is concave up and down, in terms of t.

Find all the horizontal and vertical tangent lines, in terms of t. The parametric equation x=sin⁡(𝑡) and y=cos⁡(𝑡) is given for the interval 0≤𝑡≤2𝜋, answer the questions below. Find all the horizontal and vertical tangent lines, in terms of t. Find where the parametric equations are concave up, in terms of t. Graph this on calculator and track the t-values