The graphs of the function $F$ (left, in blue) and $G$ (right, in red) are below. Let $P(x)=F(x)G(x)$ and $Q(x)=F(x)/G(x)$.
Answer the following questions.
- $P′(1)=$
- $Q′(1)=$
- $P′(6)=$
- $Q′(6)=$
Here is the graph of $y=F(x):$
And here is the graph of $y=G(x):$
I know this is asking me to be able to use the Product and Quotient rule to find the derivatives; Product rule if asking for $P'(x)$ and Quotient for $Q'(x)$. I am fairly okay with doing these two. However, I am unsure how to get the numbers I need from the graph: the $f(x), g(x)$, $f'(x)$ and $g'(x)$. I believe $f(x)$ would be $1$ and $g(x)$ would be $3$, but I am unsure–and definitely unsure about how to get the $f'(x)$ and $g'(x)$. Any help would be appreciated.
Best Answer
Since you are asked for $P'(x)$ at both $1$ and $6$, and the same for $Q'(x)$, you need to be more clear as to the values of $x$. Here is what I read straight from the graphs:
$$F(1)=1, \quad F(6)=4$$ $$G(1)=3, \quad G(6)=4$$
The derivatives are only slightly more tricky: look at the slope of the tangent line.
$$F'(1)=0, \quad F'(6)=\frac 12$$ $$G'(1)=1, \quad G'(6)=3$$