Find the exact length of the curve. Use a graph to determine the parameter interval.r=\cos^2(\theta/2)

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)
b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)
c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)
d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)
e) The coordinates of the point of inflection. $(x,y)=$

Represent the plane curve by a vector-valued function. (There are many correct answers.)
${\displaystyle 3x+4y-12=0}$

Write in Cartesian coordinates the parametric equations of the curve with polar equation ${\displaystyle r\left(t\right)=<\sqrt{t},\frac{\pi }{8}>}$.

Let ${\displaystyle A(2,1,1),B(1,2,1)}$, and ${\displaystyle C(1,1,2)}$ be three given points. Find
i) parametric and symmetric equations of the line through the point A and parallel to the line through the points B and C;

What is the polar form of (1, 3)?

Replace the polar equation with equivalent Cartesian equations. $x-y=3$

Do the lines ${\displaystyle \frac{x}{3}=\frac{y}{2}=\frac{z}{2}\text{and}\frac{x}{5}=\frac{y}{3}=\frac{z-4}{2}}$ intersect?