Relative Maximum
f'(c)=0 function increasing left of c and decreasing right of c
A relative maximum is a point on a function where the value of the function is greater than the value of the function at all nearby points, but not necessarily greater than the value of the function at all other points on the function.
For example, on the function f(x) = x^2, the point (0,0) is a relative maximum. This is because for all values of x near 0, such as -0.1, -0.001, and 0.1, the value of the function is less than it is at x=0. However, there are other points on the function, such as (1,1), where the value of the function is greater than it is at x=0, so (0,0) is not an absolute maximum.
To find relative maximums on a function, we can use the first derivative test. If the first derivative of the function changes from positive to negative at a point, then that point is a relative maximum. Alternatively, if the second derivative of the function is negative at a point, then that point is also a relative maximum.
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