Let f(x) = (8) - (6/x) + (2/x^2). Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima)
f is increasing on the intervals ____
f is decreasing on the intervals ______
The relative maxima of f occur at x = _____
The relative minima of f occur at x = _____
Thanks for any help! But if you could please write down the steps!
f is increasing on the intervals ____
f is decreasing on the intervals ______
The relative maxima of f occur at x = _____
The relative minima of f occur at x = _____
Thanks for any help! But if you could please write down the steps!
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You'd want to find the derivative of the function...
f'(x)=0-6/(x^2)-4/(x^3)
When you solve for zero, you should get x=0, x=2/3. There is no extrema at 0 because it is undefined.
At x=2/3, there is a minimum because it changes from - to +.
f is increasing where the derivative is positive, and decreasing when the derivative is negative. The derivative is seen to be increasing from (infinity, 0) and (2/3, infinity) and decreasing from (0, 2/3)
(There is no maximum in this function)
f'(x)=0-6/(x^2)-4/(x^3)
When you solve for zero, you should get x=0, x=2/3. There is no extrema at 0 because it is undefined.
At x=2/3, there is a minimum because it changes from - to +.
f is increasing where the derivative is positive, and decreasing when the derivative is negative. The derivative is seen to be increasing from (infinity, 0) and (2/3, infinity) and decreasing from (0, 2/3)
(There is no maximum in this function)