sketch a function with the given conditions. I already tried this but I don't think I did it right. How should I draw this?

Question

Point A: m_tan A>0

Point B: m_tan B=0

Point C: m_tan C<0

Point D: m_tan D is vertical.

Sorry, I know this question might be hard to explain in words.

Thanks!

Answer 1

To sketch this function, focus on the slope of the tangent line at each point. At point A, the tangent slope is positive, so draw the curve increasing from left to right. At point B, the tangent slope is zero, so the curve should be flat, like at the top of a hill or bottom of a valley. At point C, the tangent slope is negative, so the curve should be decreasing from left to right. Finally, at point D, draw the curve with a vertical tangent, meaning it becomes extremely steep and the tangent line is straight up and down.

There are many possible correct graphs, as long as each point satisfies its given slope condition.