Consider the following function \[ f(x)=7 \sin (x)+3 \cos (x), \quad 0 \leq x \leq 2 \pi \] (a) Does $x=3$ belong to an interval on which $f$ is increasing or decreasing? Increasing Decreasing (b) Determine the $x$-values for which $f$ has an absolute minimum and absolute maximum. Enter numeric values correct to 2 decimal places. absolute minimum: $x=$ Number absolute maximum $x=$ Number (c) Determine the interval on which $f$ is concave up. Enter numeric values correct to 2 decimal places.

Step 1 ：Consider the function \(f(x)=7 \sin (x)+3 \cos (x), \quad 0 \leq x \leq 2 \pi\)

Step 2 ：To determine whether the function is increasing or decreasing at \(x=3\), we need to find the derivative of the function \(f(x)\) and evaluate it at \(x=3\).

Step 3 ：The derivative of the function \(f(x)\) is \(f'(x) = -3\sin(x) + 7\cos(x)\)

Step 4 ：Evaluating the derivative at \(x=3\), we get \(f'(3) = 7\cos(3) - 3\sin(3)\)

Step 5 ：The value of \(f'(3)\) is approximately -7.35

Step 6 ：Since the derivative at \(x=3\) is negative, the function is decreasing at \(x=3\)

Step 7 ：Final Answer: The function \(f(x)=7 \sin (x)+3 \cos (x)\) is \(\boxed{\text{decreasing}}\) at \(x=3\)