- #1
tandoorichicken
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For what value of k will [tex] x + \frac{k}{x}[/tex] have a relative maximum at x= -2?
A relative maximum is a point on a graph where the value of a function is greater than all nearby points, but not necessarily the highest point on the entire graph.
To find the relative maximum of a function, you must first take the derivative of the function and set it equal to 0. Then, solve for the variable to find the x-value of the relative maximum. Plug this value into the original function to find the y-value.
The variable k represents a constant value that is added to the function. It can affect the shape and position of the graph, but does not change the overall behavior of the function.
x=-2 is specified in the question because it is the value at which we are trying to find the relative maximum of the function. By plugging in this value for x, we can solve for the y-value of the relative maximum.
No, the relative maximum at x=-2 is not necessarily an absolute maximum. It is only the highest point within a small interval around x=-2, but there may be higher points on other parts of the graph. An absolute maximum is the highest point on the entire graph.