Determine whether or not the graph of the function has a vertical tangent or vertical cusp at the indicated point c.
$f(x) = (x+2)^7/3$
I took the first derivative and chain rule and that got me.
$ f'(x) = 7/3(x+2)^4/3*1$
Then I plugged in c
$f'(-2) = 7/3(-2+2)^4/3 = 0$
Then I put that into a line graph.
Then I got
$f(1) = 2^7/3$
Thus this is a vertical cusp. Is this right or wrong?