Division requires a larger computational budget than multiplication (computers are just like us, we hate long division!), which can cause issues in responsiveness of user interfaces, framerates in videogames, and the time needed to run simulations for important engineering problems. (a) Find the linearization, L(x), of f(x) = for x near 1. (b) It can often save significant time to use the above linearization to approximate x с ≈ CL(x), x since multiplication is computationally cheaper than division. For numbers x ≈ 1 the loss in accuracy is negligible compared to the gain in efficiency.

5. At a sunglass manufacturing company, the estimated average cost function for producing a new line of glasses is C(x)=x2-4x+20, where x is the number of units produced, in thousands. C(x) is measured in dollars. Estimate the rate at which the average cost is changing at a production level of 3000 units. 3

s(x)= 2x2 t(x)= 3X (S x t)(X)= (S+t)(X)=  (S-t)(-2)=

(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.