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Question 5. Related Rates and Optimization . . . . . . . . . ....

Question 5. Related Rates and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 17 points Please answer the following questions. You need to justify your answers.

(a) Suppose that two variables x and y satisfy the equation 8x^2 +22y^2 = C for some constant C. Find dy/dx at (x, y) = (10, 5).

(b) Find the point P on the line y = 2x + 5 which is closest to the origin O and calculate the length of OP (the distance between the origin and P).

(c) Each side of a square is increasing at a rate of 14cm/s. At what rate is the area of the square increasing when the area of the square is 9cm^2 ?

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milcah answered 1 year ago
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