Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function...

Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function is differentiable everywhere. (III) If f(x) is differentiable everywhere, with f(−1) < 0, and f(2) > 0, then the equation f(x) = 0 must have a solution in the open interval (−1, 2). Which of the following is true?

(a) Only (II) is always true.

(b) Only (I) and (III) are always true.

(c) Only (II) and (III) are always true.

(d) Only (III) is always true.

(e) Only (I) is always true.

A rectangular box with square base and no top is manufactured using sheets of cardboard. The boxes will be used to store 50 cubic inches of tiny pellets that are ready for shipping. The manufacturing company intends to avoid wasting material so it is important to determine the optimal design. Let x be the length of the sides of the base given in inches. Let y be the height of the box given in inches. Which mathematical model is appropriate?

(a) Minimize 2x 2 + 4xy when 2x 2 y = 50.

(b) Minimize 2x 2 y when x 2 + 4xy = 50.

(c) Minimize 2x 2 y when 2x 2 + 4xy = 50.

(d) Minimize x 2 + 4xy when 2x 2 y = 50.

(e) None of the above.

Expert Solution

milcah answered 1 year ago

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Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function...

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