Question:
The equation of the tangent to the curve \( y = x + \frac{4}{x^2} \) that is parallel to the x-axis is
The equation of the tangent to the curve \( y = x + \frac{4}{x^2} \) that is parallel to the x-axis is
Show Hint
Horizontal tangent occurs where derivative equals zero.
Updated On: Apr 30, 2026
- \(y=1\)
- \(y=2\)
- \(y=8\)
- \(y=0\)
- \(y=3\)
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The Correct Option is B
Solution and Explanation
Concept:
Tangent parallel to x-axis means:
\[
\frac{dy}{dx}=0
\]
Step 1: Differentiate. \[ y = x + 4x^{-2} \] \[ \frac{dy}{dx} = 1 - 8x^{-3} \]
Step 2: Set slope zero. \[ 1 - \frac{8}{x^3} = 0 \Rightarrow \frac{8}{x^3} = 1 \Rightarrow x^3=8 \Rightarrow x=2 \]
Step 3: Find \(y\). \[ y=2+\frac{4}{4}=2+1=3 \] Thus tangent is: \[ y=3 \]
Step 1: Differentiate. \[ y = x + 4x^{-2} \] \[ \frac{dy}{dx} = 1 - 8x^{-3} \]
Step 2: Set slope zero. \[ 1 - \frac{8}{x^3} = 0 \Rightarrow \frac{8}{x^3} = 1 \Rightarrow x^3=8 \Rightarrow x=2 \]
Step 3: Find \(y\). \[ y=2+\frac{4}{4}=2+1=3 \] Thus tangent is: \[ y=3 \]
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