To find the linearization, we need a point, and we need a slope. So if we know that a is -2 to get the Y value, we're literally going to stick in -2 every time we see the X in the original. So -3 * -2 ^3 + 2 * -2 + 1. When we plug that through, we get 21. So we have a point of when X is -2 Y is 21. So we have our point. Now we need our slope. We get our slope by the 1st derivative. So F prime of X = -9 X squared +2. We're going to stick in the X location of -2 so -2 ^2 4 four times -9 negative 36 + 2 negative 34. We have a point, we have a slope. So we're going to find our linearization by using the point slope formula L of X = 21 plus the slope -434 times the quantity X - -2. If we multiply that out and combine our like terms, we get L of X equaling -34 X -47.