Question

the following table lists the values of functions f and g, and of their derivatives, f and g, for x = 4. let function f be defined as f(x) = f(x) · g(x). f(4) =

Explanation:

Step1: Apply the product rule

The product rule states that \((uv)^\prime = u^\prime v+uv^\prime\). For \(F(x)=f(x)g(x)\), we have \(F^\prime(x)=f^\prime(x)g(x)+f(x)g^\prime(x)\).

Step2: Substitute \(x = 4\)

Substitute \(x = 4\) into the formula for \(F^\prime(x)\). We know that \(f(4)=- 4\), \(g(4)=13\), \(f^\prime(4)=0\), and \(g^\prime(4)=8\). Then \(F^\prime(4)=f^\prime(4)g(4)+f(4)g^\prime(4)\).

Step3: Calculate the value

$$
LATEXBLOCK0
$$

Answer:

\(-32\)