1. True or False In general, if f is a continuous function, then Delta x = dx an
ID: 3109304 • Letter: 1
Question
1. True or False In general, if f is a continuous function, then Delta x = dx and Delta y greaterthanorequalto dy. 2. Fill in the blank An absolute _____ of f is a value f(c) such that f(c) greaterthanorequalto f(c) for all x in domain off f. 3. True or False Absolute extrema of a continuous function f always occur at the endpoints of a closed interval. 4. Find Delta y given y = f(x) = x - x^2, x = 3 & Delta x = 0.02 (round to four decimal places) 5. Find dy given y = x^3 + x + 2/x^2 + 3 6. A rectangular box with a square base & a cover is to have a volume of 2500ft^3. If the cost of material is $2/ft^2 for the bottom, $3/ft^2 for the top & $1/ft^2 for the sides, what should the dimensions of the box be in order to minimize the cost? 7. Find the absolute extrema given f(x) = x + 50/x; (0, infinity) 8. If R(x) = 52x - 0.5x^2 & C(x) = 22x - 1, find the maximum profit and the number of units that must be produced and sold in order to yield this maximum profit. Assume that R(x) and C(x) are in dollars. 9. Find the absolute extrema given f(x) = 1/3 x^3 - x + 2/3; (-infinity, infinity) 10. A closed-top cylindrical container is to have a volume of 250 in^2. What dimensions (radius & height) will minimize the surface area?Explanation / Answer
1. Since dx and dy stands for infinitesimle change they can't be equal to x and y respectively. (Ans: False)
2. Maxima is a value such that for given interval f(x)<= maxima (Ans: Maxima)
3. A curve can be of any shape which may contain extrema (maxima or minima) anywhere between given interval. (Ans: False)
4. y + y = f(x + x)=(x+ x) - (x+ x)^2 = x+ x - (x^2 + 2xx + x^2)
y= [x+ x - (x^2 + 2xx + x^2)] - y = [x+ x - (x^2 + 2xx + x^2)] - (x-x^2)
y=x+ x - x^2 - 2xx - x^2 - x + x^2 = x - 2xx - x^2
now put x=3 and x=0.02
y = 0.02 - 2*3*0.02 - 0.02^2 = -0.1004
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