If f(x) = `sin^(4)x+cos^(4)x+bx +c` then find possible values of b and c such that f(x) is monotonic for all `x in R.`

Explanation

To determine the values of \( b \) and \( c \) such that the function \( f(x) = \sin^4 x + \cos^4 x + bx + c \) is monotonic for all \( x \in \mathbb{R} \), we need to analyze the first derivative of the function.

### Step-by-Step Solution:

1. **Find the First Derivative:**
\[ f'(x) = \frac{d}{dx}(\sin^4 x + \cos^4 x + bx + c) \]
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