Evaluate $f(x)=\sin \left(x^{2}\right)$, and tell whether its antiderivative $F$ is increasing or decreasing at the point $x=-4$ radians.

Step 1 ：First, we need to evaluate the function \(f(x)=\sin \left(x^{2}\right)\) at \(x=-4\).

Step 2 ：We substitute \(-4\) into the function to get \(f(-4)\).

Step 3 ：Next, we need to determine whether the antiderivative \(F\) of \(f\) is increasing or decreasing at \(x=-4\).

Step 4 ：To do this, we find the derivative of \(F\), which is \(f\). If \(f(-4) > 0\), then \(F\) is increasing at \(x=-4\). If \(f(-4) < 0\), then \(F\) is decreasing at \(x=-4\).

Step 5 ：We find that \(f(-4)\) is approximately -0.288.

Step 6 ：Since \(f(-4)\) is negative, this means that the antiderivative \(F\) is decreasing at \(x=-4\).

Step 7 ：Final Answer: The value of \(f(-4)\) is approximately -0.288, and the antiderivative \(F\) is \(\boxed{\text{decreasing}}\) at \(x=-4\).