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# Find the values for which f(x) is increasing ...?

f(x)= (2x-5)^(3) +x

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- 1 month agoFavorite Answer
Find when f'(x) > 0

f(x) = (2x - 5)^3 + x

f'(x) = 3 * (2x - 5)^2 * 2 + 1

f'(x) = 6 * (2x - 5)^2 + 1

f'(x) > 0

0 < 6 * (2x - 5)^2 + 1

-1 < 6 * (2x - 5)^2

-1/6 < (2x - 5)^2

(2x - 5)^2 is always greater than or equal to 0, so this means that f(x) is always increasing.

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