## To make a graph of the given conditions, follow these steps:

1. Start by drawing a horizontal x-axis and a vertical y-axis on a piece of graph paper.

2. Plot the point (-1, f(-1)) on the graph. Since f'(-1) = 0, this point represents a local minimum. Depending on the specific function, you may need to determine the y-coordinate of this point using additional information or calculations.

3. Similarly, plot the point (1, f(1)) on the graph. Since f'(1) = 0, this point represents a local maximum. Again, you might need more information to determine the exact y-coordinate.

4. From these two points, draw a smooth curve that increases as x approaches 1 from the left and then starts to decrease after passing 1. The curve should have a steep slope near -1 and become nearly horizontal near 1 in order to represent a local minimum and a local maximum, respectively.

5. On the left side of -1, draw a smooth curve that decreases as x becomes more negative. This represents the condition that f'(x) < 0 for x < -1. The curve should have a downward slope.

6. On the right side of 1, draw another smooth curve that increases as x becomes larger than 1. This represents the condition that f'(x) > 0 for x > 1. The curve should have an upward slope.

Remember that the description above assumes a general shape for the graph based on the given conditions. The specific shape and exact y-values may depend on the function being graphed.