Question: a. If f(x) = x 4 , show that b. If f(x) = x n for positive integer n, show that c. Use the result

a. If f(x) = x4, show that


f(x +h)-f(x) h = 4x + 6xh + 4xh + h.


b. If f(x) = xn for positive integer n, show that


image


c. Use the result in part (b) in the definition of the derivative to prove the power rule:


image

f(x +h)-f(x) h = 4x + 6xh + 4xh + h.

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