C is a curve defined by the parametric equation x=t2 and y=t3-3 t. The equation of the tangent line to this curve at (4,2) is

Question

C is a curve defined by the parametric equation x=t2 and y=t3-3 t. The equation of the tangent line to this curve at (4,2) is (A) y=15 x-58 (B) y=2 (C) y=x-2 (D) y=(9 x/4)-7

Tardigrade Admin · Accepted Answer

Slope M =( dy / dx )=( dy / dt / dx / dt ) M =(3 t 2-3/2 t ) text at t =2 M =(9/4) Equation of tangent at (4,2) ⋅ M=(9/4) (y-2)=(9/4)(x-4) ⇒ y=(9/4) x-7

Q. $C$ is a curve defined by the parametric equation $x = t^{2}$ and $y = t^{3} - 3 t$ . The equation of the tangent line to this curve at $(4, 2)$ is

$y = 15 x - 58$

$y = 2$

$y = x - 2$

$y = \frac{9 x}{4} - 7$

Slope $M = \frac{d y}{d x} = \frac{d y / d t}{d x / d t}$
$M = \frac{3 t ^{2} - 3}{2 t} at t = 2$
$M = \frac{9}{4}$
Equation of tangent at $(4, 2) \cdot M = \frac{9}{4}$
$(y - 2) = \frac{9}{4} (x - 4) \Rightarrow y = \frac{9}{4} x - 7$

Q. C is a curve defined by the parametric equation x=t2 and y=t3−3t. The equation of the tangent line to this curve at (4,2) is

y=15x−58

y=2

y=x−2

y=49x​−7