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Solution for If the Tangent to the Curve Y = X3 + Ax + B at (1, − 6) is Parallel to the Line X − Y + 5 = 0, Find a and B ? - CBSE (Commerce) Class 12 - Mathematics

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Question

If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b ?

Solution

\[\text { Given }:\]

\[x - y + 5 = 0\]

\[ \Rightarrow y = x + 5\]

\[ \Rightarrow \frac{dy}{dx} = 1\]

\[\text { Now,} \]

\[y = x^3 + ax + b . . . \left( 1 \right)\]

\[ \Rightarrow \frac{dy}{dx} = 3 x^2 + a\]

\[\text { Slope of the tangent at }\left( 1, - 6 \right)= \text { Slope of the given line }\]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_\left( 1, - 6 \right) = 1\]

\[ \Rightarrow 3 + a = 1\]

\[ \Rightarrow a = - 2\]

\[\text { On substitutinga }= - 2, x=1 \text { and}y=-6 \text { in eq.} (1), \text { we get} \]

\[ - 6 = 1 - 2 + b\]

\[ \Rightarrow b = - 5\]

\[ \therefore a = - 2 \text { and} \ b = - 5\]

  Is there an error in this question or solution?
Solution If the Tangent to the Curve Y = X3 + Ax + B at (1, − 6) is Parallel to the Line X − Y + 5 = 0, Find a and B ? Concept: Tangents and Normals.
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