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If slope of curve is first positive, the...

If slope of curve is first positive, then zero and after that became negative, so best represented to following graph which satisfied above condition is :

A

B

C

D

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To solve the problem, we need to analyze the conditions given for the slope of the curve and identify the correct graph representation based on these conditions. ### Step-by-step Solution: 1. **Understanding Slope Conditions**: - The slope of the curve is first positive, which means the tangent to the curve makes an angle with the x-axis that is greater than 0 degrees and less than 90 degrees. - The slope then becomes zero, which means the tangent to the curve is horizontal, making an angle of exactly 0 degrees with the x-axis. - Finally, the slope becomes negative, meaning the tangent makes an angle greater than 90 degrees and less than 180 degrees with the x-axis. 2. **Analyzing Each Graph**: - **Graph 1**: Check if the slope is positive, then zero, and then negative. - Initially, if the curve is rising (positive slope), then it levels off (zero slope), and then it falls (negative slope). This graph satisfies all conditions. - **Graph 2**: Check if the slope is positive, then zero, and then negative. - If the curve rises but then drops immediately to a negative slope without reaching zero, this graph does not satisfy the conditions. - **Graph 3**: Check if the slope is positive, then zero, and then negative. - Similar to Graph 2, if the curve does not level off to zero before becoming negative, this graph does not satisfy the conditions. - **Graph 4**: Check if the slope is positive, then zero, and then negative. - If the curve rises, levels off to zero, and then falls, this graph satisfies all conditions. 3. **Conclusion**: - The graphs that satisfy the condition of having a positive slope, then zero slope, and finally a negative slope are Graph 1 and Graph 4. - Therefore, the best representation of the curve is Graph 1 (or Graph 4 if applicable). ### Final Answer: The best representation of the curve that satisfies the conditions is **Graph 1** (and possibly Graph 4).
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