Find equation of tangent line to f(x)

Question

a) f(x)= 2(sinx)(cosx), x=pi/6

b) f(x)= e^x(sinx), x=0

Answer 1

Hello Hoffman Estates,

 

To find the equation of a line, I like to go with point-slope form:

 

y - y₁= m(x - x₁)

 

So, now all we need is the slope, m, and a point (x₁,y₁).  Let's look at part (a):

 

- Slope:  we need the slope of the curve at x = pi/6.  Isn't the instantaneous slope of a curve its derivative, and then you plug in x at that point to find the slope?

 

- Point:  The problem says to find the tangent line at a certain x value.  So, that gives us x₁ for our line.  If the line has to touch the curve at x₁, then what does y have to equal at that value of x?

 

Now all you have to do is figure out the derivative, which has some trig in it and a product...and then part (b) works the same way, but with a different point and a different derivative.

 

Let us know if that helps get you started, and we're here for more help if you need.