Question

Just some good ole calculus

Answer 1

find f(x) if f(2)=4 and the tangent line at x has a slope of (x-1)e^(x^(2)-2x)

Answer 2

that is not a slope, that is a function
how does the question read?

Answer 3

exactly how I typed it out sadly...

Answer 4

actually could use help with a few of these, but I'll only trouble you with the one I'm currently asking about

Answer 5

ok i get what it is asking, but it was written by a moron

Answer 6

\((x-1)e^{x^2+2}\) is not the slope of anything, it is a function
what they want you to do is find the anti derivative of this thing, which you can do by a simple \(u\) - sub and then find the constant by using \(f(2)=4\)

Answer 7

typo there, should be \((x-1)e^{x^2-2x}\)

Answer 8

put \(u=x^2-2x, dyu =(2x-2)dx, \frac{1}{2}du = (x-1)dx\) and integrate
\[\frac{1}{2}\int e^udu\]

Answer 9

right away you get
\[f(x)=\frac{1}{2}e^{x^2-2x}+C\] and then you find \(C\)

Answer 10

ok yeah thanks for the help, that's what I got and now just need to find the C, if anyone wants to help with the other problems that would be awesome too

Answer 11

do you know how to find \(C
\)?

Answer 12

yes, set x=2 and the whole equation equal to 4 and then solve

Answer 13

ok then you are good to go

Answer 14

hey thanks for your help

Answer 15

yw