4. Find all local maxima and minima of the following function ƒ : R → R. Which ones are global maxima/minima? Explain. f(r) = 4 2p3 11 2 - 6x + 2 for all x E R.
Please solve the screenshot and explain how you get the global max/min (in general). Thanks!
Definition used -
Local maxima and minima - In an open interval, Maximum and minimum value of the function is called local maxima and minima respectively.
It can be found using first or second derivative tests.
Second derivative test - First we equate the first derivative to 0 and solve for x. It gives us critical values of x at which local maxima or minima occur. Then we found the second derivative and plug critical values in it.
If then there is a local minimum at x = c.
If then there is a local maximum at x =c.
Global maxima or minima- In a given interval, Maximum and minimum value of the function is called local maxima and minima respectively.
Given -
Taking the derivative of it with respect to x both sides-
These are critical values.
Step by step
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