2. +-4 points WaneAC6 5.1.011 My Notes Ask Your Teacher Locate and classify all
ID: 2912576 • Letter: 2
Question
2. +-4 points WaneAC6 5.1.011 My Notes Ask Your Teacher Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether each extremum is a relative or absolute maximum or minimum.) Also, locate any stationary points that are not relative extrema. HINT [See figure.] (Order your answers from smallest to largest x.) f has Select- at (x, y)- f has | Select , at (x, y) f ha Select t(x, y)-C a relative minimum a relative maximum an absolute minimum an absolute maximum no extremumExplanation / Answer
From the graph we can see that the slope of the graph is zero (at critical points) when x is -2 as well as when x is +2
Let's analyse now at x =-2; we see that the graph is concave upwards, i.e values of y to the left and right of x =-2 are more than the value of y at x =-2. Therefore there is certainly a relative minima at x =-2.
We can also see that no where in the given range the value is lower and further at the end point of the given range we can see that the graph is moving upwards. Hence, the value of y is an absolute minimum value at x =-2. This minimum value of y can be seen as -2.
Therefore, we can fill the first option as f has an absolute minimum at (x,y)=(-2,-2)
Next, let's look at the other critical point x =+2; here
Hence their is no minimum or maximum when x =+2; and value of y is +2
Therefore we can fill the second option as f has no extremum at (x,y)=(2,2)
Lastly let's look at the point x=-1; where we can see that the shape of the curve is changing from concave upwards to concave downwards. We also conclude this by checking the position of an imaginary tangent line; which would be below the graph just before x=-1 and above the graph just after x=-1
Hence x=-1 is the inflection point for the graph with value of y as 0.
Therefore we can fill the third option as f has no extremum at (x,y)=(-1,0)
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