Question: Assume that total national consumption is given by a function C(x), where x is the total national income. The derivative C'(x) is called the marginal

Assume that total national consumption is given by a function C(x), where x is the total national income. The derivative C'(x) is called the marginal propensity to consume. Then S = x − C represents total national savings, and S'(x) is called marginal propensity to save. Suppose the consumption function is C(x) = 8 − 0.8x − 0.8√x. Find the marginal propensity to consume, and determine the value of x that results in the smallest total savings.

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