2. Consider the function f(x) =( 1)/(x) over [1,4]. a. Find f'(x). b. Find the slope of the secant line through the endpoints. c. Find all values of x for which the function satisfies the Mean Value Theorem on the interval [1,4].
Added by Spencer G.
Step 1
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = nx^(n-1). In this case, f(x) = 1/x, so we can rewrite it as f(x) = x^(-1). Applying the power rule, we get f'(x) = -1*x^(-1-1) = -1/x^2. Therefore, Show more…
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