Let   $\displaystyle {f{{\left({x}\right)}}}={x}^{{4}}-{50}{x}^{{2}}$ .   Here is its unlabelled graph:

$\displaystyle {f{{\left({x}\right)}}}$   is increasing on the interval(s)   $\displaystyle {x}\in$   Preview Question 6 Part 1 of 7  
(Enter as an interval or union of intervals with "U" denoting union   –   example: (-2,-1) U (1,oo).)

$\displaystyle {f{{\left({x}\right)}}}$   is decreasing on the interval(s)   $\displaystyle {x}\in$   Preview Question 6 Part 2 of 7  

Local maxima of   $\displaystyle {f{{\left({x}\right)}}}$   are at  
(Enter the coordinates of each local maxima; if there is more than one, enter the coordinates, separated by commas.)

Local minima of   $\displaystyle {f{{\left({x}\right)}}}$   are at  
(Enter the coordinates of each local maxima; if there is more than one, enter the coordinates, separated by commas.)

The graph of   $\displaystyle {y}={f{{\left({x}\right)}}}$   is concave up over the interval(s)   $\displaystyle {x}\in$   Preview Question 6 Part 5 of 7  
(Enter as an interval or union of intervals with "U" denoting union   –   example: (-oo,-1) U (1,3].)

The graph of   $\displaystyle {y}={f{{\left({x}\right)}}}$   is concave down over the interval(s)   $\displaystyle {x}\in$   Preview Question 6 Part 6 of 7  

Enter here (using math notation or by attaching in an image) an explanation of your solution.