Show that function f given by `f(x)=(1)/(5)x^(5)-3x^(4)+12x^(3)+4x, x in R ` is stictly increasing on R.

Explanation

To show that the function \( f(x) = \frac{1}{5} x^5 - 3x^4 + 12x^3 + 4x \) is strictly increasing on \( \mathbb{R} \), we need to find the derivative \( f'(x) \) and demonstrate that it is positive for all \( x \in \mathbb{R} \).

### Step-by-Step Solution:

1. **Find the Derivative \( f'(x) \)**:
\[ f(x) = \frac{1}{5} x^5 - 3x^4 + 12x^3 + 4x \]
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