a. find the derivative of f at x. that is, fi...

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