Derivatives, Tangents: y = 6secx - 12cosx at pt (pi/3, 6)

[Casas4]

Ok so here is the problem I am having.I understand derivatives for the most part however, I have come across several homework problems where it asks me to find the tangent line using such and such points. Here is the question I am struggling with.

Find the equation of the tangent line to the curve y = 6 sec x - 12 cos x at the point ( pi/3 , 6). The equation of this tangent line can be written in the form y = mx+b
where m is?
and b is?

I solved the derivative down to

6(2sin[x]+sec[x]tan[x])

I guess i dont know where to go from here or even if i needed to derive that equation. I know at some point you need to you point use slope intercept form y-y1=m(x-x1) and plug in the point pi/3 and 6.

 

[PAULK]

Re: Derivatives and Tangent Lines help please

Ok so here is the problem I am having.
I understand derivatives for the most part however, I have come across several homework problems where it asks me to find the tangent line using such and such points.
Here is the question I am struggling with.
Find the equation of the tangent line to the curve y = 6 sec x - 12 cos x at the point ( pi/3 , 6). The equation of this tangent line can be written in the form y = mx+b
where m is?
and b is?
I solved the derivative down to
6(2sin[x]+sec[x]tan[x])
I guess i dont know where to go from here or even if i needed to derive that equation. I know at some point you need to you point use slope intercept form y-y1=m(x-x1) and plug in the point pi/3 and 6.

Then you are almost there! So you have y - 6 = m(x - pi/3) and if you could just get that pesky, m, which is the slope, out of there, you would have it. Perhaps you can remember some sentence that combined the words "slope" and "derivative".

 

[Casas4]

Re: Derivatives and Tangent Lines help please

can i use the limit as a approaches 0 of f(x)-f(a)/x-a thats the only thing i can remember
Casas4

 

[skeeter]

Re: Derivatives and Tangent Lines help please

can i use the limit as a approaches 0 of f(x)-f(a)/x-a thats the only thing i can remember
Casas4

why would you want to do that when you already have the derivative ?

I solved the derivative down to

6(2sin[x]+sec[x]tan[x])

sub in \(\displaystyle \frac{\pi}{3}\) for x and evaluate the value of the slope at the point \(\displaystyle \left(\frac{\pi}{3}, 6\right)\)