Consider the line y=2x+5
a. Find a function f so that f`=y above and f(0)=0
b. Derive a function A(t) which gives the area of the parallelogram bounded by the x-axis, the line y=2x+5, the line x=0 and the line x=t.
c. What is the relationship between the functions f and A?

Question

anonymous · Answer

So I believe I have figured out part a.

f(x)=x^2+5x

anonymous · Answer

Completely stumped on b...

amistre64 · Answer

the line x=t?

anonymous · Answer

Yeah, i don't know what line x=t is either.... THat's all I'm given.

Oh and f(x)=x^2+5x+C, (forgot constant)

amistre64 · Answer

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anonymous · Answer

what is the x intercept of t?

amistre64 · Answer

the area is:

$$\int_{0}^{t} 2x+5\ dx$$

amistre64 · Answer

t is an arbitrary number

anonymous · Answer

Yeah, i see now.

anonymous · Answer

Hmm, okay thats pretty simple. Thanks!

amistre64 · Answer

we could also do it with simple geometric stuff; but the calc looks neater lol

anonymous · Answer

What is the relationship between F and A?

anonymous · Answer

Is it just that f shows the rate at which the area of A changes?

amistre64 · Answer

hmmm, i got no good answer for that .... f(x) is the derivative of the area sounds good.  but i dunno