In which interval is the given function f(x) | vedclass

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(B) Given function: $f(x) = 2x^3 - 15x^2 + 36x + 1$. Find the derivative: $f'(x) = \frac{d}{dx}(2x^3 - 15x^2 + 36x + 1) = 6x^2 - 30x + 36$. Factor the

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$(2, 3)$

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(B) Given function: $f(x) = 2x^3 - 15x^2 + 36x + 1$. Find the derivative: $f'(x) = \frac{d}{dx}(2x^3 - 15x^2 + 36x + 1) = 6x^2 - 30x + 36$. Factor the derivative: $f'(x) = 6(x^2 - 5x + 6) = 6(x - 2)(x - 3)$. For the function to be monotonically decreasing,we must have $f'(x) So,$6(x - 2)(x - 3) This inequality holds when $x$ lies between the roots $2$ and $3$. Therefore,the interval is $(2, 3)$.

In which interval is the given function $f(x) = 2x^3 - 15x^2 + 36x + 1$ monotonically decreasing?

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