Calculus 1 : How to describe points by graphing functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #1 : Describing Points

Graph 20150721 185534

 

Suppose a point on the curve given above has the property that 

Based solely on the graph above, which of the following is most likely the  value of the point in question?

Possible Answers:

Correct answer:

Explanation:

If then the graph must be concave up at the point. Based on the picture, we know that the curve is concave up on  at best. The only value that falls on this interval is , which is . Since , this definitely falls on the interval given and we can be sure it is concave up based on the picture.

Example Question #2 : Describing Points

What is the critical point for ?

Possible Answers:

Correct answer:

Explanation:

To find the critical point, you must find the derivative first. To do that, multiply the exponent by the coefficient in front of the  and then subtract the exponent by . Therefore, the derivative is: . Then, to find the critical point, set the derivative equal to .

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