x-value for the steepest part of a slope

Galleria Mace
Galleria Mace used Ask the Experts™
How would I find the x-value where the slope is the steepest for this sine graph (the blue one in bold)?
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This is very straight forward: The derivative of sin, which is cos, describes the slope of the sin at every value.

The steepest slopes of sin(x) occur at x=0 (slope= 1) and x=pi (slope= -1).

For your function, f is the amplitude of the sinusoid, and sets the value of the maximum slope.

g is the frequency of the sinusoid and h is the phase (or x) offset.  g and h determine the location of the maximum slope.

i is the y offset.  It has nothing to do with the magnitude of location of the maximum slope.

The maximum slope of 4 occurs when g(x+h) = 0, or x = -h/g = -1.6/0.22 = -7.273.  But that is not what you have plotted.

And by the way, there is something wrong with plot for x values between 15 and 25.  It should be a valley, not a hill.


Thanks for the help!! And yeah I added that hill at x=15 to x=25, it was for the design of the task

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