Thread: linear appx/graph reading

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

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

Originally Posted by cassiopeia1289

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

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 .

For b): The value of the function is the length of the segment .

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 ??
and what are they even asking for d - and actual number?

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 ??
and what are they even asking for d - and actual number?

For part c, you use the tangent line at to approximate the value of the function at . In the drawing you have, this approximation is given by the length of . But the formula for this approximation is , which simplifies to in this case.

For part d, this is simply . It doesn't help you a whole lot except that as h approaches zero, this is the derivation of the derivative of at a.