G-Solve

G-Solve is a graphical solving tool which allows you to find key features on a graph, including:

• x-intercepts.
• y-intercepts.
• Maximum of minimum points (turning points).
• Global (function) maximum or minimums.

Other actions and commands are also possible beyond this list - these will be introduced later.

Worked Example 1:

The features of G-Solve will be illustrated using the function f: ℝ → ℝ, f(x) = x² + 3x - 10:

Figure 1 - The features available in the G-Solve list.

x-intercepts

To find the x-intercepts use "Root" from the G-Solve list:

Figure 2 - The x-intercepts (y = -10) found using the y-intercept command in G-Solve.

Therefore, the coordinates of the y-intercept are (0,-10).

y-intercepts

To find the y-intercept(s) use "y-intersect" from the G-Solve list:

Figure 3 - The y-intercept (x = -5 and x = 2) found using the Root command in G-Solve.

Therefore, the coordinates of the y-intercept are (0,-10).

Turning points

To find the turning point use "Min" or "Max" options from the G-Solve list:

Figure 4 - The turning point found using Min/Max command in G-Solve.

Therefore, the coordinates of the turning point are (-1.5, 12.25).

Note: G-Solve is a numerical tool; therefore, all answers given are decimalised and will not necessarily be exact. To find exact answers you need to refer to the main program.

Worked Example 2:

Additional features of G-Solve will be illustrated using the function f: [-1,2] → ℝ, f(x) = x²:

Function minimum

To find the function (global) minimum use "fMin" from the G-Solve list:

Figure 5 - The function minimum found using the fMin command in G-Solve.

Therefore, the coordinates of the function minimum are (0,0).

Function maximum

To find the function (global) maximum use "fMax" from the G-Solve list:

Figure 6 - The function maximum found using the fMax command in G-Solve.

Therefore, the coordinates of the function maximum are (2,4).

Note: Using the function minimum and function maximum commands we can determine the range of a function. for the function f: [-1,2] → ℝ, f(x) = x² the range is [0,4].