# linear appx/graph reading

• April 28th 2008, 03:01 PM
cassiopeia1289
http://i26.tinypic.com/r8fddg.png
ok, I am completely at a loss - I don't even know where to begin.
for (a): I should find the slope of T - but I have no idea how - could I make a triangle and solve for the hyp? so would it be like $f'(a) = \sqrt{PQ^2 + QT^2}$

and then I am at a complete loss, partially because the given diagram is so confusing ... any help would be greatly welcomed
• April 28th 2008, 03:08 PM
icemanfan
Quote:

Originally Posted by cassiopeia1289
http://i26.tinypic.com/r8fddg.png
ok, I am completely at a loss - I don't even know where to begin.
for (a): I should find the slope of T - but I have no idea how - could I make a triangle and solve for the hyp? so would it be like $f'(a) = \sqrt{PQ^2 + QT^2}$

and then I am at a complete loss, partially because the given diagram is so confusing ... any help would be greatly welcomed

For a): The slope of the tangent line is equal to $\frac{QT}{PQ}$.

For b): The value of the function is the length of the segment $RS$.
• April 29th 2008, 01:59 PM
cassiopeia1289
any hints as to how to answer c and d?
those are where I am absolutely at a loss -
c: I mean, would you find like ${f(h) - f(a)}/(h-a)$??
and what are they even asking for d - and actual number?
• April 29th 2008, 02:07 PM
icemanfan
Quote:

Originally Posted by cassiopeia1289
any hints as to how to answer c and d?
those are where I am absolutely at a loss -
c: I mean, would you find like ${f(h) - f(a)}/(h-a)$??
and what are they even asking for d - and actual number?

For part c, you use the tangent line at $(a, f(a))$ to approximate the value of the function at $a + h$. In the drawing you have, this approximation is given by the length of $ST$. But the formula for this approximation is $y = f(a) + f'(a)(x - a)$, which simplifies to $f(a) + f'(a)\cdot{h}$ in this case.

For part d, this is simply $\frac{f(a + h) - f(a)}{h}$. It doesn't help you a whole lot except that as h approaches zero, this is the derivation of the derivative of $f(x)$ at a.