How is it going guys? I have a test next week and there are a couple of questions on my test review that I don't understand. Here they are:
1. For what values of x does the graph f have a horizontal tangent.
a. f(x)= x + 2cosx b. f(x)= (e^x) (sinx)
- Regarding these problems, I know how to find the derivative, but have no idea what to do next to solve it.
2. Let f(x)=x-2cosx, where x is greater than or equal to 0, but less than or equal to 2 pie.
a. On what intervals is f increasing or decreasing?
b. On what intervals is f concave upward or concave downward?
3. Find equations of both lines that are tangent to the curve y=1+x^3 and parallel to the line 12x-y=1.
Help or any feedback would be greatly appreciated, thanks.
2. Let f(x)=x-2cosx, where x is greater than or equal to 0, but less than or equal to 2 pie.
a. On what intervals is f increasing or decreasing?
b. On what intervals is f concave upward or concave downward?
Ok, so we want examine the derivative of the function on the interval . If , then the function is increasing. If , then the function is decreasing.
If , then the function is concave upward.
All you have to do is solve the inequality and then right the answer in interval notation:
Now just draw a graph of the sine function and plot the points on the curve. You'll see that the function is greater than on the intervals:
Therefore, the function f is increasing on this interval.