use the fact that the derivative of the function f(x) = 4/x is f(x) = -4/x^2 to find the equation of the…

use the fact that the derivative of the function f(x) = 4/x is f(x) = -4/x^2 to find the equation of the tangent line to the graph of f(x) at the point x = -5. the equation of the tangent line to the graph of f(x) at the point x = -5 is .

use the fact that the derivative of the function f(x) = 4/x is f(x) = -4/x^2 to find the equation of the tangent line to the graph of f(x) at the point x = -5. the equation of the tangent line to the graph of f(x) at the point x = -5 is .

Answer

Explanation:

Step1: Find the slope of the tangent line

The slope $m$ of the tangent line is the value of the derivative at the given point. Substitute $x = - 5$ into $f'(x)=\frac{-4}{x^{2}}$. $m=f'(-5)=\frac{-4}{(-5)^{2}}=-\frac{4}{25}$

Step2: Find the y - coordinate of the point on the curve

Substitute $x=-5$ into $f(x)=\frac{4}{x}$. $f(-5)=\frac{4}{-5}=-\frac{4}{5}$

Step3: Use the point - slope form of a line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-5,-\frac{4}{5})$ and $m =-\frac{4}{25}$. $y-(-\frac{4}{5})=-\frac{4}{25}(x - (-5))$ $y+\frac{4}{5}=-\frac{4}{25}(x + 5)$ $y+\frac{4}{5}=-\frac{4}{25}x-\frac{4}{5}$ $y=-\frac{4}{25}x-\frac{8}{5}$

Answer:

$y =-\frac{4}{25}x-\frac{8}{5}$