Question
Download Solution PDFThe equation of the tangent to the curve x3 + y2 + 3y + x = 0 and passing through the point (2, -1).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Steps to find the equation of the tangent to the curve:
Find the first derivative of f(x).
Use the point-slope formula to find the equation for the tangent line.
Point-slope is the general form: y - y₁=m(x - x₁), Where m = slope of tangent =
Calculation:
Given curve x3 + y2 + 3y + x = 0
Differentiating w.r.t x
3x2 + 2y
(2y + 3)
At (2, -1)
The equation of the tangent is
(y - (-1)) = -13(x - 2)
y + 1 = -13x + 26
y + 13x - 25 = 0
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