Let `f(x)=2x^(3)-3(a+b)x^(2)+6abx`. If ` a gt b` , determine the local maximum / minimum points of f(x). If a=b, how will the answer change ?

Explanation

To find the local maximum and minimum points of the function \( f(x) = 2x^3 - 3(a+b)x^2 + 6abx \), we will follow these steps:

### Step 1: Find the derivative of \( f(x) \)
We start by differentiating \( f(x) \):
\[ f'(x) = \frac{d}{dx}(2x^3 - 3(a+b)x^2 + 6abx) \]
Using the power rule, we get:
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