Sketch the graph y=X3-2x-5x+6

Online "^" is used to indicate an exponent, e.g., x^2 = x squared.

Cannot sketch on these posts.

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To sketch the graph of y = x^3 - 2x^2 - 5x + 6, you can follow these steps:

1. Determine the x-intercepts: To find the x-intercepts, we set y = 0 and solve for x. In this case, we need to solve the equation x^3 - 2x^2 - 5x + 6 = 0. You can use various methods to find the roots, such as factoring, using the Rational Root Theorem, or numerical methods like graphing calculators or software.

2. Determine the y-intercept: The y-intercept occurs when x = 0. Plug x = 0 into the equation y = x^3 - 2x^2 - 5x + 6 and find the corresponding y-value.

3. Find critical points: Critical points occur where the derivative of the function is zero or undefined. Take the derivative of y = x^3 - 2x^2 - 5x + 6 and set it equal to zero. Solve for x to find the critical points.

4. Determine the behavior near critical points: Determine whether the function is increasing or decreasing near each critical point by evaluating the sign of the derivative on either side of the critical point.

5. Sketch the graph: Use the information gathered from steps 1-4 to plot the x-intercepts, y-intercept, critical points, and behavior near the critical points. You can also evaluate additional points by substituting different x-values into the equation. Connect the dots to form a smooth curve.

Since this is a long process to explain and it involves calculations, it would be best if you sketch the graph using graphing tools or software that can easily plot the equation and provide a visual representation in a graph.