Find an equation for the tangent line to the curve y=8/sqrt(4+3x) at the point (4,2). The derivative is -12/sqrt(4+3x)^3/2. I'm looking for an equation with ?x +/- ?y = ?. I keep getting a fraction for x and I can't have a fraction at all.

Question

Find an equation for the tangent line to the curve y=8/sqrt(4+3x) at the point (4,2).  The derivative is -12/sqrt(4+3x)^3/2. I'm looking for an equation with ?x  +/- ?y = ?.  I keep getting a fraction for x and I can't have a fraction at all.

anonymous · Answer

so you want to know an equation of the line of the tangent right?

anonymous · Answer

yes

anonymous · Answer

ie in the form y = mx + c

I am going to assume that your differentiation is write, ie you have already done the hard bit.
Put x = 4 into your derivative.gives you m.

anonymous · Answer

I did and a fraction pops out.  I can't have a fraction.  do you know if I did some wrong?

anonymous · Answer

as long as the differentiation is write then you are fine, a fraction is only a number. You could if you wanted write this as a decimal but its easier to keep it as a fraction

So from here write your equation y = mx + c, you have found m, doesn't mater if it is a fraction.  then use what you know about the point on the curve you were given to calculate c

anonymous · Answer

So what did you get for m?

anonymous · Answer

-3/5

anonymous · Answer

ok so$$y = \frac{ -3 }{ 5 }x +c$$
right
what is the coordinates of the point you are given

anonymous · Answer

(4,2)

anonymous · Answer

so y = 2 and x = 4, so now re right the equation and solve for c

anonymous · Answer

I get 4.4

anonymous · Answer

ok so your equation is:$$y = \frac{ -3 }{ 5 }x + 4.4$$
this looks good but i have just checked your answer by doing it myself and i think you have made a small calculation error.

because i get -3/16 as the gradient ie m.

So this is not the exact write answer but your differentiation is correct so hey you have done the hard part and all you need to do is redo the C calculation.

anonymous · Answer

I get y=3/16x+11/4

anonymous · Answer

could I rewrite that any other way b/c I'm given multiple choice and that is not one of them.

anonymous · Answer

ah, right so the equation you have is: $$ y = \frac{-3}{16}x + \frac{11}{4}$$
You know that 4^2 is 16 so if you times the entire equation by 16 is that one of your options?

anonymous · Answer

I would get 3x+16y=44 and yes that is one of them! thank you, yet why or how did you know to do 4^2?

anonymous · Answer

mostly from what you told me at the very start, i can't have a fraction, then when you told me it was multiple choice I then saw why you didn't think it could be a fraction.

simply because none of your answers were fractions, then basically I just took the the largest denominator (bottom bits of fractions, in this case 16) and timed the equation by that.
 
also because questions that teachers set are not usually full of coincidences, unlike real life. So when you see a number like say 3 and then a square of that number 9, i always start thinking about what they might get me do to.

Any way sorry for the essay hope it helps.

anonymous · Answer

it did thank you so much