f(x)=2x^2; a. find f inverse c. evaluate df/dx at x=5 and df(inverse)/dx at x=f(5)

Question

lgbasallote · Answer

f(x) = 2x^2

to find the inverse..the first step is to change f(x) into y, yes?

anonymous · Answer

yes

lgbasallote · Answer

so you ahve

y = 2x^2

now...solve for x..do you know how to?

anonymous · Answer

$$y=\sqrt{x/2}$$

lgbasallote · Answer

what did you do? why did you swap the variables?

lgbasallote · Answer

remember... if you start out with y = then the inverse would be x = 

got it?

anonymous · Answer

$$f ^{-1}=\sqrt{x/2}$$

anonymous · Answer

$$f ^{-1}(x)=\sqrt{x/2}$$

lgbasallote · Answer

nevermind what i said earlier...my source (ahem @TAKEBACKMATH ) told me the inverse should be x =... $$y = \sqrt{\frac x2}$$
^that's right

anonymous · Answer

that's not really the part I needed help with...it is evaluating the derivative at x=5 and the inverse derivative at x=f(5)....do you know how to do that?

lgbasallote · Answer

do you know the derivative of 2x^2?

anonymous · Answer

4x?

lgbasallote · Answer

right. now substitute x = 5

anonymous · Answer

do I have to use the quotient rule to figure out the derivative of $$\sqrt{x/2}$$

lgbasallote · Answer

nope.. youse constant multiple rule $$\sqrt{\frac x2} \implies \frac{\sqrt x}{\sqrt 2}$$
it's just the same as $$\frac 1{\sqrt 2} (\sqrt x)$$

lgbasallote · Answer

so your coefficient is 1/sqrt 2... just take the derivative of sqrt x

lgbasallote · Answer

then multiply to 1/sqrt 2

lgbasallote · Answer

anyway... i have to leave now...so i hope you luck

anonymous · Answer

ahhh...thank you!!!

lgbasallote · Answer

welcome