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)=-121/x^2 b. the slope of the tangent line at x = - 11 is

Answer

# Explanation: ## Step1: Recall derivative formula The derivative of $\frac{u}{x}$ (where $u$ is a constant) is $-\frac{u}{x^{2}}$. Here $u = 121$, and we already know from part a that $f'(x)=-\frac{121}{x^{2}}$. ## Step2: Substitute $x=-11$ Substitute $x = - 11$ into $f'(x)$. We get $f'(-11)=-\frac{121}{(-11)^{2}}$. ## Step3: Simplify the expression $(-11)^{2}=121$, so $f'(-11)=-\frac{121}{121}=-1$. # Answer: -1