A sign diagram is a way of visualizing a curve’s graph by indicating the inflection points, stationary points, and the increases or decreases in the curve.
First, set up a horizontal line with a matching indicator of either a stationary or an inflection point from the graph
Notice that a stationary/turning point exists at 00. Hence, the line is marked 00 at a location that matches the graph
Next, get the derivative of the function to identify the gradients of parts of the curve
f(x)f(x)
==
x2x2
f′(x)
=
2x
Note that if x≥0 or positive, f′(x) is also positive, which means the curve’s slope is increasing
Indicate this on the sign diagram by adding a positive sign to the right of 0
Also note that if x≤0 or negative, f′(x) is also negative, which means the curve’s slope is decreasing
Indicate this on the sign diagram by adding a negative sign to the left of 0
A sign diagram is a way of visualizing a curve’s graph by indicating the inflection points, stationary points, and the increases or decreases in the curve.
First, set up a horizontal line with a matching indicator of either a stationary or an inflection point from the graph
Notice that a stationary/turning point exists at 0. Hence, the line is marked 0 at a location that matches the graph
Next, get the derivative of the function to identify the gradients of parts of the curve
f(x)
=
x3
f′(x)
=
3x2
Note that since the power of x is even, f′(x) will always be positive regardless of the sign of x. This means the curve’s slope is always increasing
Indicate this on the sign diagram by adding a positive sign to the left and right of 0
A sign diagram is a way of visualizing a curve’s graph by indicating the inflection points, stationary points, and the increases or decreases in the curve.
First, set up a horizontal line with a matching indicator of either a stationary or an inflection point from the graph
Notice that an inflection point exists at 0 and a stationary point exists at 3. Hence, the line is marked 0 and 3 at a location that matches the graph
Next, notice that the curve’s slope decreases at the left side of 0
Indicate this on the sign diagram by adding a negative sign to the left of 0
Also, the curve’s slope decreases at the right side of 0
Indicate this on the sign diagram by adding a negative sign to the right of 0
Lastly, notice that the curve’s slope increases at the right side of 3
Indicate this on the sign diagram by adding a positive sign to the right of 3
A sign diagram is a way of visualizing a curve’s graph by indicating the inflection points, stationary points, and the increases or decreases in the curve.
First, set up a horizontal line with a matching indicator of either a stationary or an inflection point from the graph
Notice that an inflection point exists at 0 and a stationary point exists at -1 and 2. Hence, the line is marked -1,0 and 2 at a location that matches the graph
Next, notice that the curve’s slope increases at the left side of -1
Indicate this on the sign diagram by adding a positive sign to the left of -1
Then, the curve’s slope decreases at the right side of -1
Indicate this on the sign diagram by adding a negative sign to the right of -1
Still, the curve’s slope decreases at the right side of 0
Indicate this on the sign diagram by adding a negative sign to the right of 0
Lastly, notice that the curve’s slope increases at the right side of 2
Indicate this on the sign diagram by adding a positive sign to the right of 2
