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TANGENTS AND NORMALS if the tangent to the curve y=x^3 + ax + b at (1, -6) is parallel to the line x – y + 5 = 0 find a and b

TANGENTS AND NORMALS
if the tangent to the curve y=x^3 + ax + b at (1, -6) is parallel to the line x – y + 5 = 0 find a and b

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

Slope of tangent at (1, -6) = 1 (Given from slope of line)
y = x^3 + ax + b
y' = 3x^2 + a
1 = 3 + a
a = -2

Put in the curve equation, we have
-6 = 1 -2 + b
b = -5

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