Question

For what value of x, the function \(f(x) = 2x^3 + 3x^2 - 36x + 10\) has minimum

• A. -2
• B. -3
• C. 2
• D. 1

Hint:

For a cubic polynomial with two critical points, the smaller x-value (more negative) typically corresponds to the local maximum, and the larger x-value corresponds to the local minimum, assuming a positive leading coefficient. This can be a quick check.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Evaluate (1/x)∂z/∂x + (1/y)∂z/∂y for z=x²-y².

Step 2: Key Formula (Alternate):
Find partial derivatives treating other variable as constant, then substitute.

Step 3: Detailed Explanation:
∂z/∂x=2x, ∂z/∂y=-2y. Expression = (1/x)(2x)+(1/y)(-2y) = 2-2 = 0.

Step 4: Final Answer:
Value is 0.