I need to find the slope of the graph of the function at the given point.
Function:
f(theta)=4sin(theta)-(theta)
Point:
(0,0)
I tried finding the derivative of the function at theta=0, but I got 0 for an answer.
I checked the answer in the back of my book and it is 3.
I just need to figure out how to get there.
Thanks to anyone who tries to help me.
--Cori
The derivative of f(theta) is
f'(theta) = 4 cos(theta) -1
When theta = 0, the value of the derivative is 4 -1 = 3.
Only one question: How did you get -1 from -theta ?
Thanks so much!
The derivative of f(thetha) = theta is
f'(theta) = df/d(theta) = 1. It's the same thing as saying the derivative of
f(x) = x is f'(x) = 1.
Thanks so much. I get it now.
To find the slope of the graph of the function at the given point, you need to find the derivative of the function and evaluate it at the given point.
Let's start by finding the derivative of the function f(theta). The derivative of 4sin(theta) is 4cos(theta), and the derivative of -(theta) is -1. Therefore, the derivative of the function f(theta) is given by:
f'(theta) = 4cos(theta) - 1
Now, to find the slope at the point (0,0), substitute theta = 0 into the derivative:
f'(0) = 4cos(0) - 1
Since cos(0) equals 1, this simplifies to:
f'(0) = 4(1) - 1
= 4 - 1
= 3
So the slope of the graph of the function at the point (0,0) is 3.
It seems that you may have made an error when taking the derivative. Double-check your work and make sure you correctly applied the differentiation rules. The correct derivative should give you the slope of 3 at (0,0).