SOLUTION: Hi, first of all I'm not sure if this is the right category or not but the question is: Find the approxmiate value of the tangent to the following functions at the given x-val

Question 245178: Hi, first of all I'm not sure if this is the right category or not but the question is:

Find the approxmiate value of the tangent to the following functions at the given x-value. Use the algebraic method.
A) y = 1/x at x = 1
B) y = 3cos3x at x = 3

I have 2 similar questions but I think once I get a grasp from thsoe 2 i can follow the steps for the other ones... Can you please show me the answer for these questions and show your work so I can do questions in the future similar to this.
Thanks :)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the approxmiate value of the tangent to the following functions at the given x-value. Use the algebraic method.
A) y = 1/x at x = 1
y' = -1/x^2 which is the equation of the tangent.
@ x = 1, y' = -1 which is the slope of the tangent.
You said "value of the tangent", I'm not sure what that is.
-----------------
B) y = 3cos3x at x = 3
y' = -9sin(3x)
at x = 3, y' = -9sin(9)
=~ -3.709066
I assumed x is in radians. If not, it will have to be converted before the function is differentiated.
---------------
I don't know what the "algebraic method" is. You can use this info to check your answers, if nothing else.

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