Find the absolute maximum and minimum values of a function `f` given by `f(x)=2x^3-15 x^2+36 x+1` on the interval `[1,\ 5]` .

Explanation

To find the absolute maximum and minimum values of the function \( f(x) = 2x^3 - 15x^2 + 36x + 1 \) on the interval \([1, 5]\), we will follow these steps:

### Step 1: Find the derivative of the function
We start by calculating the first derivative of the function \( f(x) \).

\[ f'(x) = \frac{d}{dx}(2x^3 - 15x^2 + 36x + 1) \]
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