Question

Math help plz

Answer 1

Find the equation of the tangent line to the curve in the day-plane given by \[x^3+y^3 = 9 \]

Answer 2

Do I need to use the implicitly differentiation to find the derivative first, then plugin the x-value ...as given in the question...to find the instantaneous rate of change at that point ...once I have the slope, points.. I can use the y = my+b equation to write the equation of the tangent line correct?

Answer 3

@DuarteME

Answer 4

I mean plugin both x and y values in to the implicitly differentiation and get my instantaneous rate of change at that particular point...

Answer 5

I got dry/do = -x^/y^2 as an answer to that equation... so far.. now i’m Going to plugin the points into the derivative

Answer 6

Let me draw what I did..one second plz

Answer 7

/

Answer 8

Well, in this case, we are dealing with cubics and they are invertible everywhere, so you can solve the equation for \(y\) and find \(\frac{\textrm{d}y}{\textrm{d}x}\). This might not be so easy in general. For instance, say you are dealing with a curve defined by \(y\textrm{e}^{xy} = 3x\).

Implicit differentiation is also okay and you'll probably get the answer faster. Your work seems fine so far. (:

Answer 9

Thanks master. Really appreciated your feedback. God bless you!! <3 :)
I will post the final answer in a bit. :)

Answer 10

Nice job! You seem to have lost the \(x\) just before the arrow, but other than that it looks great!

Answer 11

Oh yeah...sorry lol...thanks master! *BOWS*.

Answer 12

Now i’m Going to start the applications of derivatives ...where the graph is increasing and decreasing and stuff... in the next chapter.. :)