Question $4.$ Divide the rectangle above representing $f(t+h)*g(t+h)$ into $4$ pieces: One should represent

$f(t)*g(t)f(t+h)$ and $f(t)as$ a small 'nudge' $of$ the function $(or$ output$)f,att,i.e.df.$ Write $an$

expression for the area $of$ the largest rectangle $in$ terms $of$ the $4$ smaller rectangles.

Question $5.We$ can use the $limit$ definition $of$ the derivative here $to$ find the derivative $of$ the product.

Writing out the definition $of$ the derivative $we$ see

$\frac{d}{(d)t}(f(t)*g(t))=\underset{h0}{lim}\frac{f(t+h)g(t+h)-f(t)g(t)}{h}$

What does the numerator $of$ the fraction represent $in$ terms $of$ the rectangles you have drawn? How can

you interpret the $limit?$

Question $6.$ Using your answer from the last question, how does the product rule appear $in$ your answer

$to$ Question $4?$ What you have should almost $be$ the product rule but with one additional term. Make $a$

conjecture $(the$ mathematical word for guess$)asto$ why this term can $be$ ignored?