9514 1404 393
Answer:
a = 36
Explanation:
A stationary point is where the function derivative is zero. Here, we have ...
y' = 2kx -16/x^2 = 0
For x = 2/3, this is ...
4/3k -16/(4/9) = 0
4/3k = 36
k = 27
Then the value of y at that point is ...
y = 27(2/3)^2 + 16/(2/3) = 12 +24 = 36
The stationary point of interest is (2/3, a) = (2/3, 36). a = 36.