a. find the slope of the tangent line to the graph of f at the given point. b. find the slope - intercept…

a. find the slope of the tangent line to the graph of f at the given point. b. find the slope - intercept equation of the tangent line to the graph of f at the given point. f(x)=2x^2 - 2x at (2,4) a. the slope is . (type an integer or a simplified fraction.)

a. find the slope of the tangent line to the graph of f at the given point. b. find the slope - intercept equation of the tangent line to the graph of f at the given point. f(x)=2x^2 - 2x at (2,4) a. the slope is . (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Find the derivative of f(x)

The derivative of $f(x)=2x^{2}-2x$ using the power - rule $\frac{d}{dx}(x^{n}) = nx^{n - 1}$ is $f^\prime(x)=4x-2$.

Step2: Evaluate the derivative at the given x - value

We want to find the slope of the tangent line at the point $(2,4)$. Substitute $x = 2$ into $f^\prime(x)$. So $f^\prime(2)=4\times2-2$. $f^\prime(2)=8 - 2=6$.

Step3: Find the equation of the tangent line

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m = 6$ and the line passes through the point $(2,4)$. Substitute $x = 2$, $y = 4$ and $m = 6$ into $y=mx + b$: $4=6\times2 + b$. Solve for $b$: $4 = 12 + b$, then $b=4 - 12=-8$. The equation of the tangent line is $y = 6x-8$.

Answer:

a. 6 b. $y = 6x-8$