Find a vector equation and parametric equations for the line

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. $(x,y)=$

Sketch the parametric curve for the following set of parametric equations. Clearly indicate direction of motion
1)${\displaystyle x=5\cos t}$
2)${\displaystyle y=2\sin t}$
3)${\displaystyle 0\ge t\ge 2\pi }$

1) Find the area of the part of the plane
$4x+3y+z=12$
that lies in the first octant.
2) Use polar coordinates to find the volume of the given solid.
Bounded by the paraboloid ${\displaystyle z=5+2x^2+2y^2}$ and the plane z = 11 in the first octant

Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique.
The line segment starting at ${\displaystyle P(-1,-3)}$ and ending at ${\displaystyle Q(6,-16)}$

Represent the line segment from P(-2, -3, 8), Q(5, 1, -2) by a vector-valued function and by a set of parametric equations.

Let ${\displaystyle P\left(x\right)=F\left(x\right)G\left(x\right)}$ and ${\displaystyle Q\left(x\right)=\frac{F\left(x\right)}{G\left(x\right)}}$, where F and G are the functions whose graphs are shown.
a) Find ${\displaystyle P^{\prime }\left(2\right)}$
b) Find ${\displaystyle Q^{\prime }\left(7\right)}$

Find the maximum rate of change of f at the given point and the direction in which it occurs.
${\displaystyle f(x,y)=4y\sqrt{x},(4,9)}$
maximum rate of change =
direction vector =