Question

If y=(x)/(x+1)+(x+1)/(x), then (d²y)/(dx²) at x=1 is equal to:

• A. \( \dfrac{7}{4} \)
• B. \( \dfrac{7}{8} \)
• C. \( \dfrac{1}{4} \)
• D. -(7)/(8)

Hint:

Simplify the function before differentiating to reduce errors.

Answer 1

The Correct Option is D

Step 1: Simplify y=(x)/(x+1)+(x+1)/(x)=1-(1)/(x+1)+1+(1)/(x) =2+(1)/(x)-(1)/(x+1)
Step 2: Differentiate (dy)/(dx)=-(1)/(x²)+(1)/((x+1)²)
Step 3: Second derivative (d²y)/(dx²)=(2)/(x³)-(2)/((x+1)³)
Step 4: At x=1 (d²y)/(dx²)=2-(2)/(8)=(14)/(8)-(2)/(8)=-(7)/(8)