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Describe how the graph of $f$ varies as $c$ varies. Graphseveral members of the family to illustrate the trends that youdiscover. In particular, you should investigate how maximum and minimum points and inflection points move when $c$ changes. You should also identify any transitional values of $c$ at which the basic shape of the curve changes.$$f(x)=c x+\sin x$$

When $c=0,$ the function becomes $y=\sin x$ . When $c$ is not zero, the function has exactly oneincercept at origin. When $|c|>1,$ there is no local minima or maxima. When $c$ increases, theabsolute value of the function also increases. As $|c|$ increases, the function comes closer to the$y$ - axis. The transitional value is 1 .

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

Campbell University

Baylor University

University of Michigan - Ann Arbor

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there are a couple of varieties of dysfunction. Draft here for different see values like negative one and zero and positive one, and you'll notice that the maxes and men's will change depending on what she is. And so those will be at different X values. However, the con cavity will remain the same because if you imagine taking the second derivative, then this term here no longer matters. And so you're left with just this. And so that's a way Algebraic lee to show that the con cavity does change, however, Sorry the con cavity stays the same at the same Max values can cavity is constant, but the maxes and men's change and then you can see the general shape so as um, X values become more positive. The graph slants up this way. Um, it eventually kind of comes down clockwise and then matches up with CIA. Zero continues going clock waas until when you get really big negative values, then it starts going this direction. So, really, you could just kind of picture that turning of clockwise as your values become mawr negative. Of course, we could just do the opposite way as well. Here

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