Question

Consider the following function.f(x)=x-2 sin (x)

Find f(2) and f(4)= For what values of x does the graph of f have a horizontal tangent?

Answer 1

To find f(2) and f(4), substitute x = 2 and x = 4 into the function f(x) = x - 2 sin(x). To find the values of x where the graph of f has a horizontal tangent, find where the derivative of f(x) is equal to 0.

Step-by-step explanation:

To find the value of f(2), we substitute x = 2 into the function f(x) = x - 2 sin(x):

f(2) = 2 - 2 sin(2)

To find the value of f(4), we substitute x = 4 into the function:

f(4) = 4 - 2 sin(4)

To find the values of x where the graph of f has a horizontal tangent, we need to find the values of x where the derivative of f(x) is equal to 0. The derivative of f(x) can be found using the chain rule: