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Unformatted text preview: 4.1 36 . a.) We know that at x=3 there is a critical value which means that at x=3 the slope is zero. Were given that f(1)=3 and f(5)=-1. Therefore, we know that the slope is increasing to the left of x=3, the slope is zero at x=3, and the slope is decreasing after x=3. This means that at x=3 we have a local maximum. A possible graph of the function is given below. b.) As x approaches infinity and as x approaches negative infinity, the limits are both infinity. Therefore, if there is only one critical point, this graph has to be a parabola and x=3 must be the minimum value since the values on either side approach infinity. A possible graph of the function is given below. c.) Before and after x=3 the slopes are both positive. Since there is a critical point at x=3 the concavity of the slope has to change there. Since the slope is positive on both x=3 the concavity of the slope has to change there....
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