What is C if f(2)=1/3?

Question

#f'(x)= (5x-5)^2#. Find C if #f(2)=1/3#

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Answer 1 · 2018-03-12T20:05:53

#c = -49/3#

#f'(x) = (5x-5)^2#

#(5x-5)^2 = 25x^2-50x+25#

#f'(x) = 25x^2-50x+25#

#nx^(n-1) = 25x^2 rarr x^n = 25/3x^3#

#nx^(n-1) = -50x rarr x^n = -50/2x^2 = -25x^2#

#nx^(n-1) = 25 rarr x^n = 25x#

#f(x) = 25/3x^3 - 25x^2 + 25x + c#

where #c# is a constant.

#25/3x^3 - 25x^2 + 25x# can be factorised to give #25x(1/3x^2 - x + 1)#

#f(x) = 25x(1/3x^2 - x + 1) + c#

#f(2) = 50(4/3 - 2 + 1) + c#

#= 50/3 + c#

#f(2) = 50/3 + c = 1/3#

#c = 1/3 - 50/3 = -49/3#