Question
Download Solution PDFThe equation of tangent to the curve y = x2 + 4x + 1 at (-1, - 2) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
To determine the equation of a tangent to a curve:
Step. 1) Find the derivative of given curve
Step. 2) Calculate the gradient of the tangent at given point.
Step. 3) Determine the equation of tangent.
Substitute the gradient of the tangent and the coordinates of the given point into the gradient-point form of the straight line equation
Calculations:
Given equation of curve is y = x2 + 4x + 1.
Step. 1) Find the derivative of given curve
Differentiate w.r.to x on both side, we get
Step. 2) Calculate the gradient of the tangent at given point
⇒ m =2 (- 1) + 4
⇒ m = 2
Step. 3) Determine the equation of tangent.
Substitute the gradient of the tangent and the coordinates of the given point into the gradient-point form of the straight line equation.
⇒ (y +2) = 2(x+ 1)
⇒ 2x - y = 0
Hence, the equation of tangent to the curve y = x2 + 4x + 1 at (-1, -2) is 2x - y = 0
Last updated on Jul 1, 2025
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