At what value(s) of x does f(x) = -x4 + 2x2 have a relative maximum? (4 points)

x = -1 ,+1

Step-by-step explanation:

Let y be a function of x given in question

Simply differentiate it to get it's derivative and then equate to zero to find it's extremams.

Now equate it's derivative to zero.

=0

So, after solving we get

x=0,1,-1

Now by graphical interpretation we can observe that it is even function thus it is symmetric about Y axis. Also it passes through origin.

At minus and plus infinity of x y tends to minus infinity.

Also check nearby values to 1 or -1.

Thus at -1 and +1 there is maxima symmetrically.

The amount invested at 4% is $4,200. This problem can be solved by using two linear equation with two different variables which represent the investment's partition and the investment's return. The first equation is x+y=$7,600 and the second equation is 0.04x + 0.05y=$338, then you must substitute the y variable in the second question with the first equation (0.04x + 0.05($7,600-x)=$338). Therefore, you will get a new equation to solve the problem which is 0.04x+380-0.05x=338 resulting x=$4,200.