Question:
The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is
The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is
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For tangent equation, first find slope using derivative and then use \(y-y_1=m(x-x_1)\).
Updated On: May 7, 2026
- \(3x-y+2=0\)
- \(x-10y-50=0\)
- \(3x-y-2=0\)
- \(x-10y+50=0\)
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The Correct Option is C
Solution and Explanation
Step 1: Given curve: \[ y=x^3 \]
Step 2: Differentiate: \[ \frac{dy}{dx}=3x^2 \]
Step 3: At \(x=1\): \[ m=3(1)^2=3 \]
Step 4: Equation of tangent: \[ y-y_1=m(x-x_1) \] \[ y-1=3(x-1) \] \[ y-1=3x-3 \] \[ 3x-y-2=0 \] \[ \boxed{3x-y-2=0} \]
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