What do you know about the range of sin(x) ?appplejack said:Homework Statement
f(x)=x — cosx, 0 ≤ x ≤ 2∏
Homework Equations
The Attempt at a Solution
I took the derivative of the function: f'(x)=1+ sinx, 0 ≤ x ≤ 2∏
I don't know how to determine whether it is increasing or decreasing between the interval given. What should I do?
So... Have you solve the original problem?appplejack said:The Range of sin(x) is -1≤ x ≤ 1?
I have an additional question:
I saw this in my textbook and don't understand why this is true.
f (x) = -2sin2x — 2sinx = -2sinx(2cosx+1) <— how is this true?
Thanks
A function is a mathematical relationship between two variables, where each input (or independent variable) has only one output (or dependent variable).
A function is increasing if its output (or dependent variable) increases as the input (or independent variable) increases. A function is decreasing if its output decreases as the input increases.
A local maximum is the highest point on a specific section of a function, while a global maximum is the highest point on the entire function. A global maximum can also be referred to as an absolute maximum.
Critical points are the points where the derivative of a function is equal to zero or undefined. To find these points, you can set the derivative of the function equal to zero and solve for the input value(s).
The first derivative test states that if the derivative of a function is positive at a point, then the function is increasing at that point and the point is a local minimum. If the derivative is negative at a point, then the function is decreasing at that point and the point is a local maximum.