a. find the slope of the tangent line to the graph of f(x)=x² - 2 at the point (2,2)\nb. find the slope…

a. find the slope of the tangent line to the graph of f(x)=x² - 2 at the point (2,2)\nb. find the slope - intercept equation of the tangent line to the graph of f(x)=x² - 2 at the point (2,2).\na. what is the slope of the tangent line?\nm_tan = □

a. find the slope of the tangent line to the graph of f(x)=x² - 2 at the point (2,2)\nb. find the slope - intercept equation of the tangent line to the graph of f(x)=x² - 2 at the point (2,2).\na. what is the slope of the tangent line?\nm_tan = □

Answer

Explanation:

Step1: Find the derivative of the function

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

Step2: Evaluate the derivative at the given x - value

To find the slope of the tangent line at $x = 2$, substitute $x = 2$ into $f^\prime(x)$. So $m_{tan}=f^\prime(2)=2\times2 = 4$.

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 $m = 4$ and the line passes through the point $(2,2)$. Substitute $x = 2$, $y = 2$ and $m = 4$ into $y=mx + b$: $2=4\times2 + b$. Solving for $b$ gives $b=2-8=-6$. So the equation of the tangent line is $y = 4x-6$.

Answer:

a. $m_{tan}=4$ b. $y = 4x-6$