a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of…

a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)=121/x;x = - 11,x = 1 a. f(x)=

a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)=121/x;x = - 11,x = 1 a. f(x)=

Answer

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{121}{x}$ as $f(x)=121x^{- 1}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. Here, $a = 121$ and $n=-1$. So, $f^\prime(x)=121\times(-1)x^{-1 - 1}$.

Step3: Simplify the derivative

$f^\prime(x)=-121x^{-2}=-\frac{121}{x^{2}}$.

Answer:

$-\frac{121}{x^{2}}$