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The equation of tangent to the curve y = x2 + 4x + 1 at ( - 1, –2) is(A) 2x – y = 0 (B) 2x + y - 5 = 0 (C) 2x – y – 1 = 0 (D) x + y - 1 = 0 |
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Answer» (A) 2x - y = 0 Equation of the curve is y = x2 + 4x + 1 Differentiating w.r.t. x, we get \(\frac{dy}{dx} = 2x + 4\) ∴ Slope of tangent at (-1, -2) is \((\frac{dy}{dx})_{(-1,-2)}\) = 2(-1) + 4 = -2 + 4 = 2 Equation of tangent is y - y1 = \((\frac{dy}{dx})_{(x_1,y_1)}\) (x-x1) Here, (x1, y1) ≡ (-1, -2) ∴ [ y - (-2)] = 2[x - (-1)] ∴ y + 2 = 2(x + 1) = 2x + 2 ∴ 2x - y = 0 |
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