In which of the following intervals is the fu | vedclass

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(D) To find the interval where the function $f(x) = 2x^3 - 15x^2 + 36x + 1$ is strictly decreasing,we find its derivative $f'(x)$.$f'(x) = \frac{d}{dx

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$(2, 3)$

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(D) To find the interval where the function $f(x) = 2x^3 - 15x^2 + 36x + 1$ is strictly decreasing,we find its derivative $f'(x)$.$f'(x) = \frac{d}{dx}(2x^3 - 15x^2 + 36x + 1) = 6x^2 - 30x + 36$.For the function to be strictly decreasing,we must have $f'(x) $6x^2 - 30x + 36 Dividing by $6$,we get $x^2 - 5x + 6 Factoring the quadratic expression,we get $(x - 2)(x - 3) The inequality $(x - 2)(x - 3) Therefore,the function is strictly decreasing in the interval $(2, 3)$.

In which of the following intervals is the function $f(x) = 2x^3 - 15x^2 + 36x + 1$ strictly decreasing?

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