Question

Equation of tangent to the curve \[ y=x+\frac{4}{x^2} \] which is parallel to \(x\)-axis is

• A. \(y=8\)
• B. \(y=0\)
• C. \(y=3\)
• D. \(y=2\)

Hint:

A tangent parallel to the \(x\)-axis has slope \(0\). Hence, put \(\frac{dy}{dx}=0\) and then find the corresponding point on the curve.

Answer 1

The Correct Option is C

Step 1: Find where the tangent is horizontal.
\(y = x + 4x^{-2}\). \(\dfrac{dy}{dx} = 1 - \dfrac{8}{x^3} = 0 \Rightarrow x^3 = 8 \Rightarrow x=2\).

Step 2: Find y at x = 2.
\(y = 2 + \dfrac{4}{4} = 2+1 = 3\).

Step 3: State the tangent equation.
Tangent is parallel to x-axis at \((2,3)\): \(y = 3\).
\[ \boxed{y = 3} \]