need help

Question

need help

anonymous · Answer

attachment

amistre64 · Answer

$$f(x) = \frac{(2x+3)}{(3x-2)}$$ we need to find its derivative

amistre64 · Answer

we also need to determine the value of f(1)

anonymous · Answer

yes, but how  would take the derivative with that function?

amistre64 · Answer

by using what is so adequately refered to as:  the quotient rule

amistre64 · Answer

Do you know the derivative rules yet?

amistre64 · Answer

we could also get by with bringing the bottom to the top and placing a negative exponent on it and derive it with the product rule

anonymous · Answer

Well we haven't cover the quotient rule yet, but if you could use it to show me I would appreciate because I believe my professor was going to cover, but ran out of time

amistre64 · Answer

$$\frac{top}{bottom}$$
$$Dx\ (\frac{t}{b}) = \frac{bt'-b't}{b^2}$$

amistre64 · Answer

does that make sense as written?

anonymous · Answer

yes

amistre64 · Answer

good, find the derivates of the top and the bottom, then plug them into the right spots in the formula

anonymous · Answer

attachment

amistre64 · Answer

keep attantion to your signs; youve got some mismatched

amistre64 · Answer

its good form except for you should have (3x-2), not (3x+2).

amistre64 · Answer

unless of course i mistyped the original :)

amistre64 · Answer

when you have it all squared away, find f'(1) by using x=1 in the derivative to find the value of the slope of the tangent line at f(1)

anonymous · Answer

I get f(1)=-13

anonymous · Answer

what do I do next?

amistre64 · Answer

i got -14 .... you sure?

amistre64 · Answer

lol ... its -13

amistre64 · Answer

that is the slope of the tangent line; use it in the slope point form of an equation

amistre64 · Answer

y-f(1) = f'(1)(x-1)

anonymous · Answer

I got y=-13x+18

anonymous · Answer

did you get the same?

amistre64 · Answer

y-f(1) = f'(1)(x-1)

y-5 = -13x +13 .. yes

anonymous · Answer

yes

anonymous · Answer

whats next?

amistre64 · Answer

thats it, you found the equation of the tangent line at 1,f(1)

amistre64 · Answer

just match it to one of the formats they present

amistre64 · Answer

id go with C myself

anonymous · Answer

But c has a positive 13 in front of the x and our answer has -13 front of the x

amistre64 · Answer

y = -13x + 18
+13x    +13x
-----------------
13x+y =  18

amistre64 · Answer

you have to move stuff around to match what they present

anonymous · Answer

Thank you!