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Trace or copy the graph of the given function $ f $. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of $ f' $ below it.
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Calculus 1 / AB
Limits and Derivatives
The Derivative as a Function
Missouri State University
Oregon State University
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
Trace or copy the graph of…
So in this question were given a graph of a function asked and asked to trace your copy it and then asked to use the method example, one to sketch the graph of the derivative below it. So first of all months do the graph of F. X. This is why. And we see this graph of F. Do something like this. Okay, now then the first thing we notice is that up here at the maximum The slope of the Tangent Line is zero. Fix it up a little bit better here. Okay, knicks, I want to hear this is F this is going to be a prime madrilena That slope is zero, which means that point is here, isn't it? At zero? Okay, so starting from the left over here, what do we see? We have a slope of this, the tangent lines right? Which is nearly zero over here to start with nearly zero here then is positive and hit some maximum value here and goes back 40 here, doesn't it? Okay, so we started out at some zero value, hit some max and come back down to zero, don't we? Okay, what do we see on the other side? Well here we see that this is a decreasing curve. So these are all on the right hand side, these are all gonna be negative on the slopes, aren't they, On the derivatives. And they started out near zero, go to some maximum as we're near this inflection point here and then Come back towards zero again, don't they? As we get further down. So what do we see. Okay, so we started out near zero, right, went to some big negative number and then come back towards zero. And so we end up with a curve like that for the derivative there.
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