Question

Use the curve sketching procedure to analyze the function. a. y=x3+x2−20x b. y=1−x21+x2

Answer 1

Use the curve sketching procedure to analyze the given functions and plot the curves on a graph.

Step-by-step explanation:

Curve sketching procedure for function a:

1. Find the x-intercepts by solving for x when y = 0.
2. Find the y-intercept by evaluating the function at x = 0.
3. Find the critical points by taking the derivative and setting it equal to zero.
4. Determine the intervals where the function is increasing or decreasing by analyzing the sign of the derivative.
5. Determine the concavity by taking the second derivative and analyzing its sign.
6. Sketch the curve using the information obtained.

Curve sketching procedure for function b:

1. Follow the same steps as function a to find the intercepts, critical points, intervals of increase/decrease, and concavity.
2. Plot the curve using the obtained information.