A question from a university entrance exam says the following:
Which values of $k$ give a maximum at $x = -1$ for $f(x) = (k + 1)x^4 - (3k + 2)x^2 - 2kx$?
It seems the question may have been asked before but with a mistake in the given function.
My initial response was to calculate $f(-1)$, but this works out to be $-1$, with no $k$ involved to calculate a maximum.
Doesn't this mean that for any value of $k$, $f(-1)$ will always be $-1$, if so I don't understand how a maximum could be calculated for a variable which has no effect on the output.
This is probably a fundamental misunderstanding of the question by me.