8. Let f(x,y) = 3y2 ln(x3 + 4) + 2y/x for x > 0 and y any real number. What value of y minimizes the partial derivative of f with respect to x, when x = 2?
|
A. -1 |
B. –1/3 |
C. 0 |
|
D. 1/12 |
E. 1 |
Solution: The answer is D
The partial derivative of f with respect to x is,
When x = 2,
To find the value of y that minimizes the above equation, differentiate the above result with respect to y and find the zero of that solution. That is, solve the equation, (d/dy)(3y2 – y/2)=0, as follows:
