Find both the maximum and the minimum value of `3x^4-8x^3+` `12 x^2-48 x+1` on the interval `[1,4]` .

Explanation

To find both the maximum and minimum values of the function \( f(x) = 3x^4 - 8x^3 + 12x^2 - 48x + 1 \) on the interval \([1, 4]\), we will follow these steps:

### Step 1: Find the derivative of the function
First, we need to calculate the derivative of the function \( f(x) \).

\[ f'(x) = \frac{d}{dx}(3x^4 - 8x^3 + 12x^2 - 48x + 1) \]
...