Question

(1 point) Functions of the form f(x)= x, where n= 1,2, 3.., are often called power functions (a) Use the limit definition of the derivative to find f'() for f(x)x. fx) (b) Use the limit definition of the derivative to find f '(x) for f(x) = f'(x) (c) Use the limit definition of the derivative to find f'(x) for f(x) = x.(Hint : (a + b) +4ab +b. Apply this rule to (x + h a +4ab+6a b within the limit definition.) f'x)= (d) Based on your work in (a), (b), and (c), what do you conjecture is the derivative of f(x)=? Off(x)x? (e) Conjecture a formula for the derivative of f(x)= x that holds for any positive integern. That is, given f(x) x where n is a positive integer, what do you think is the formula for f'(x)? f'(x) =

Answer 1

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