. I am supposed to find critical numbers from this graph. I have read the solution. It says to find the critical numbers I have to find to horizontal tangency of the graph. I know that horizontal tangent has a slope of zero. and thats why the x-value of those points are the critical points. Atleast I hope I understand. But what is horizontal tangents and how come -5, -1 and 4 are horizontal tangents. I hope I don't sound stupid and I have made my question clear. Thanks in advance.
[Math] How does the graph shows horizontal tangency,but how
calculusderivatives
Best Answer
A horizontal tangent line is a line that is tangent to the curve at a point where $f'(x) = 0$.
Recall that the derivative of a point on a curve is the slope of the line tangent to that curve at that point.
For example, the horizontal line tangent to the curve at $(-5, f(-5)) = (-5, 3)$ just touches the curve. It is given, simply, by the equation of the line $y = f(-5) = $. 3(Recall that horizontal lines, having no slope, are all of the form $y = a$ for some constant a.
The values you give are not the equations of tangent lines. You need to write your tangent lines using equations $y = f(-5),\; y = f(-1), \;y = f(4)$.