Another question..
f'(x)=1/XSQRED + 2X and goes through (-1,1).
I need to find a function that has that derivative and passes through that point
Hello, Super Mallow!
$\displaystyle f'(x)\:=\:\frac{1}{x^2} + 2x$ and goes through (-1,1).
Find a function that has that derivative and passes through that point.
We have: .$\displaystyle f'(x) \;=\;x^{-2} + 2x$
Integrate: .$\displaystyle f(x) \;=\;-x^{-1} + x^2 + C \;=\;-\frac{1}{x} + x^2 + C$
We are told that, when $\displaystyle x = -1,\:f(\text{-}1) = 1$
. . So we have: .$\displaystyle -\frac{1}{\text{-}1} + (\text{-}1)^2 + C \;=\;1\quad\Rightarrow\quad C \:=\:-1$
Therefore: .$\displaystyle f(x)\;=\;-\frac{1}{x} + x^2 - 1$