Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

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

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

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    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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