How do you find and simplify #f(x+h)-f(x)# and #(f(x+h)-f(x))/h# given #f(x)=7x^2-1#?

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Answer 1 · 2016-10-23T14:55:42

Please see the explanation for the process.

Given:
#f(x) = 7x^2 - 1#

#f(x + h) = 7(x + h)^2 - 1#

#f(x + h) = 7(x^2 + 2xh + h^2) - 1#

#f(x + h) = 7x^2 + 14xh + 14h^2 - 1#

#f(x + h) - f(x) = 7x^2 + 14xh + 14h^2 - 1 - (7x^2 - 1)#

#f(x + h) - f(x) = 14xh + 14h^2#

#(f(x + h) - f(x))/h = (14xh + 14h^2)/h#

#(f(x + h) - f(x))/h = 14x + 14h#