Question

Please help me with a question that involves derivatives! I'm not sure what to do

Answer 1

Equation of tangent line of f(x) at x=a:
\(y = f'(x)(x-a)+f(a)\)

Answer 2

f'(a), not f'(x) sorry

Answer 3

when you are finding the derivative of a function you are essentially finding the slope of the tangent of the original function. so at x=pi the slope is -1 which you found to be.

Answer 4

so is a tangent line is linear you have to form a y=mx+b equation

Answer 5

you found the slope of the line to -1. all you need to find is the y-intercept

Answer 6

Okay. Which point would I use to find the y-intercept?

Answer 7

If I used geerky24's method, would the answer be y=3x-3pi+3??

Answer 8

y = sin(x) + 3
when x = pi, y = sin(pi) + 3 = 3. (pi, 3) is a point on the graph.

Answer 9

the point you are given

Answer 10

y = sin(x) + 3
when x = pi, y = sin(pi) + 3 = 3. (pi, 3) is a point on the graph.
y' = cos(x)
when x = pi, y' = cos(pi) = -1. Slope of the tangent at x = pi is -1
y = mx + b
y = -x + b and it has the point (pi, 3)
3 = -pi + b
b = (3+pi)
y = -x + pi + 3 is the equation of the tangent.

Answer 11

Oh. Okay. And I just did the problem using geerky24's method and I got the equation to be y=-x+pi+3. I forgot to do the derivative.

Answer 12

Ohh Okay!! You guys are awesome!! Thanks so much for helping!!

Answer 13

You are welcome.

Answer 14

Hey guys! I have another question. Here is the work that I did. I thought that I was doing the problem correctly, but the answer in the textbook is different from what I got.

Answer 15

would be best to post it as a new question and close this question