The tangent to the curve $y=x^3-11 x+5$ at $x=2$ is parallel to :

(A) $y=x+1$
(B) $y=-x+2$
(C) $2 y=x+3$
(D) $2 y=2 x+4$

Choose the correct answer from the options given below :

(A), (D) Only

$y = x^3 - 11x + 5$

so $y' = 3x^2 - 11$ (slope of curve is derivative)

at x = 2    $\left.y'\right]_{x=2}= 3(2)^2 - 11 = 12 - 11 = 1$

slope = 1 → it is parallel to line having slope (1)

lines with some slopes are parallel to curve at that point