Show that the derivative of the function `f` given by `f(x)=2x^3-9x^2+12 x+9` , at `x=1` and `x=2` are equal.

Explanation

To show that the derivatives of the function \( f(x) = 2x^3 - 9x^2 + 12x + 9 \) at \( x = 1 \) and \( x = 2 \) are equal, we will first find the derivative \( f'(x) \) and then evaluate it at the two points.

### Step 1: Find the derivative \( f'(x) \)

The derivative of a function can be found using the power rule. The power rule states that if \( f(x) = ax^n \), then \( f'(x) = n \cdot ax^{n-1} \).

For our function:
\[
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