posted by Phil .
I have the equation:
cos x - x = f(x)
I am told to find the relative extrema. I am also told to use the Second Derivative Test where applicable.
My question is how do I solve this problem, and how do I know when to use the Second Deriv test?
Points where the first derivative is zero are relative maxima if the second derivatve is negative and relative minima if the second derivative is positive.
In your case, df/dx = 0 when f'(x) = -sin x -1 = 0; sin x = -1
That happens when x = 3 pi/2.
At that point, f''(x) = -cos x = 0
So the second derivative fails to show if is a maximum or minimum. 3 pi/2 could be an inflection point, where the curve flattens out and then resumes its downward trend
Can't i figure out if its increasing or decreasing using the first derivative test?
What is the point of the second derivative test?