calculus problem help

[giuly]

i need help finding the line that is tangent to the curve y=sin(3?x/2) at x = 4, im not sure on how to start the problem. If someone could help me i would really appreciate it.

 

[Deleted member 4993]

i need help finding the line that is tangent to the curve y=sin(3?x/2) at x = 4, im not sure on how to start the problem. If someone could help me i would really appreciate it.

The slope of the tangent line = y'(4)

The tangent line passes through (4,y(4))

What is the point-slope form of equation of a line?

And you have it ......

 

[BigGlenntheHeavy]

$\displaystyle f(x) \ = \ sin\bigg(\frac{3\pi x}{2}\bigg) \ at \ x \ =4, \ y \ = \ 0.$

$\displaystyle f \ ' \ (x) \ = \ \frac{3\pi}{2}cos\bigg(\frac{3\pi x}{2}\bigg).$

$\displaystyle f \ ' \ (4) \ = \ \frac{3\pi}{2} \ = \ m$

$\displaystyle Ergo, \ y-0 \ = \ \frac{3\pi}{2}(x-4) \ = \ \frac{3\pi x}{2}-6\pi$

$\displaystyle See \ graph \ below.$

[attachment=0:r0ig6zqg]xyz.jpg[/attachment:r0ig6zqg]