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)f'(x)
==
2x2x
Note that if x≥0x≥0 or positive, f′(x)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 00
Also note that if x≤0x≤0 or negative, f′(x)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 00
Question 2 of 4
2. Question
Create a sign diagram for the curve f(x)=x3f(x)=x3
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)
==
x3x3
f′(x)f'(x)
==
3x23x2
Note that since the power of xx is even, f′(x)f'(x) will always be positive regardless of the sign of xx. 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 00
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 00 and a stationary point exists at 33. Hence, the line is marked 00 and 33 at a location that matches the graph
Next, notice that the curve’s slope decreases at the left side of 00
Indicate this on the sign diagram by adding a negative sign to the left of 00
Also, the curve’s slope decreases at the right side of 00
Indicate this on the sign diagram by adding a negative sign to the right of 00
Lastly, notice that the curve’s slope increases at the right side of 33
Indicate this on the sign diagram by adding a positive sign to the right of 33
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 00 and a stationary point exists at -1−1 and 22. Hence, the line is marked -1,0−1,0 and 22 at a location that matches the graph
Next, notice that the curve’s slope increases at the left side of -1−1
Indicate this on the sign diagram by adding a positive sign to the left of -1−1
Then, the curve’s slope decreases at the right side of -1−1
Indicate this on the sign diagram by adding a negative sign to the right of -1−1
Still, the curve’s slope decreases at the right side of 00
Indicate this on the sign diagram by adding a negative sign to the right of 00
Lastly, notice that the curve’s slope increases at the right side of 22
Indicate this on the sign diagram by adding a positive sign to the right of 22