Does e^(2x)(x^(2)-2) have a maximum?

The answer key says it doesn’t and the graph makes sense but then how come it passes the first derivative test and has a zero slope goes from positive to negative on the other sides also I did the second derivative tests and it concaves down
Also I wasn’t supposed to use a graphing calculator

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

that would be a prism, if not right, feel free to correct me

where is the graph or the picture? ?