I have attempted to sketch the curve of the first derivative of this function and i ended up with a piecewise function graph. However, i am unsure whether the edges of the curve touching the x- axis will have a vertical tangent or not. So how do i sketch the derivatives of a graph of this nature?
Sketch the first and second derivative of this curve
calculusderivativesgraphing-functions
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Best Answer
At the left end, the slope is nearly $+\infty$. It decreases til it looks like it's about $1$. So I'd put a vertical asymptote at the left end of the interval, and draw a curve coming down from $+\infty$ to $1$ at the point where the function has the sharp point. After that, the slope looks like it's about $-2/3$, so I'd sketch a vertical line at $y=-2/3$ over the interval between the two sharp points of the graph. Then it looks like the slope is about $1$ and it gets steeper, so I put another asymptote at the right end and draw a curve starting at $1$ and shooting up to $+\infty.$