Question

question let y(x)=f(x)⋅g(x). use the product rule to find y(8) if f(8)= - 9, f(8)=8, g(8)=0, g(8)= - 3. provide your answer below: f(x)=□

Explanation:

Step1: Recall product - rule formula

The product - rule states that if $y(x)=f(x)\cdot g(x)$, then $y^{\prime}(x)=f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$.

Step2: Substitute $x = 8$ into the product - rule formula

We know that $f(8)=-9$, $f^{\prime}(8)=8$, $g(8)=0$, and $g^{\prime}(8)=-3$. Substituting these values into $y^{\prime}(x)=f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$ at $x = 8$, we get $y^{\prime}(8)=f^{\prime}(8)g(8)+f(8)g^{\prime}(8)$.

Step3: Calculate the value of $y^{\prime}(8)$

$y^{\prime}(8)=(8\times0)+(-9\times(-3))$. First, $8\times0 = 0$. Second, $-9\times(-3)=27$. Then $y^{\prime}(8)=0 + 27=27$.

Answer:

$27$