searching for some help solving/understanding these 3 problems

2. g(x)=x^2-4x+9

a. find g'(x) = (2x-4)

b. find equation of line that is tangent to the graph of g at x = 4 (idk what to do here)

c.at what value of x is the slope = to 0 (idk what to do here. possibly set slope = to 0?)

5]f(x)= (x^2-1) / (x^2+1)

a. find f'(x) = (4x/x^4+2x^2+1)

b. is the function value of f changing more rapidly are x=0 or x=-2
(i solved for f'(0) and f'(-2). f(-2) gave me -8/25 and f'(0) gave me 0. so i think the answers x=-2?)

c. whats the equation of the line tangent to the graph at x=1

8.x^2+3y^2=4y

a. use implicit differentiation to find dy/dx (i came up with y'= -x/3y-2.... not too sure how right i am)

b. determine slope at (0,0) and (-1,1)

c. equation for tangent line at (1.1)



Thanks in advance for any help.. really appreciate it.

This post was edited by known954 on Oct 20 2013 11:24am

g'(x) is the derivative or the slope of the function at x

for the tangent like, you plug in 4 into g'(x) and find the slope of the function at 4, then plug 4 into the original equation to find y at that point

You now have x, y, and m for the equation y = mx + b, solve for b and you have your tangent line

For c, set g'(x) equal to zero and solve for x

If those are the right numbers, then you would be right that the answer is x=-2

Tangent same as described above

for #8...

implicitly differentiate you get

2x dx/dx + 6y dy/dx = 4 dy/dx
dy/dx(6y-4) = 2x, dy/dx = x/(3y-2) you were correct

for b, plug in to your dy/dx equation
for c, same as above

thank you cleared up alot of my confusion, but


b. when i plug in (-1,1) i got 1
when i plug in (0,0) i got 0/0 (which is equal to 0?)

c. idk where to plug what in, i must show work

(0,0) means y=0, x=0, so your dy/dx equation has x's and y's...so plug them in

Should have used a Moon Matrix!

This post was edited by Azrad on Oct 20 2013 02:56pm

are you still hung up on that?

clearly you took it more seriously then i did

You took it seriously enough to post it in the science section. You took it seriously enough to try to defend it. You took it seriously enough to imply I didn't know what I was talking about. And yes, I'm taking it seriously enough to rub your nose it in. Bad dog, bad dog!

This post was edited by Azrad on Oct 21 2013 01:16am