2. at what point on the graph of $f(x)=x^{2}-4$ is the tangent line parallel to the line $6x - 3y = 2$?\n(a)…

2. at what point on the graph of $f(x)=x^{2}-4$ is the tangent line parallel to the line $6x - 3y = 2$?\n(a) $(1,-3)$ (b) $(1,2)$ (c) $(2,0)$ (d) $(2,4)$

2. at what point on the graph of $f(x)=x^{2}-4$ is the tangent line parallel to the line $6x - 3y = 2$?\n(a) $(1,-3)$ (b) $(1,2)$ (c) $(2,0)$ (d) $(2,4)$

Answer

Explanation:

Step1: Find the slope of the given line

Rewrite (6x - 3y=2) as (y = 2x-\frac{2}{3}). The slope (m = 2).

Step2: Find the derivative of (f(x))

Using the power rule, if (f(x)=x^{2}-4), then (f^{\prime}(x)=2x).

Step3: Set the derivative equal to the slope of the line

Set (2x = 2), solving for (x) gives (x = 1).

Step4: Find the (y) - value

Substitute (x = 1) into (f(x)=x^{2}-4), (f(1)=1^{2}-4=-3).

Answer:

A. ((1,-3))