ECET2e Section 2.4 21/10/2016, 02:30 WebAssign ECET2e Section 2.4 (Homework) Current Score : 6 / 16 Thu Aung MATH-UA 121, section 11, Fall 2016 Instructor: Benjamin Harrop-Griffiths Due : Thursday, October 20 2016 05:00 PM EDT 1. 1/1 points | Previous AnswersSEssCalcET2 2.4.004. Differentiate. f(x) = 4 x sin x f '(x) = 4(12xsin(x)+x cos(x)) 2. 1/1 points | Previous AnswersSEssCalcET2 2.4.013. Differentiate. y= x6 4 x5 y' = 24x5x10(4x5)2 https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 1 of 6 ECET2e Section 2.4 21/10/2016, 02:30 3. 1/1 points | Previous AnswersSEssCalcET2 2.4.016. Differentiate. g(t) = t t t1/8 g'(t) = (78t((18)))38t(((58))) 4. 0/1 points | Previous AnswersSEssCalcET2 2.4.021. Differentiate. f() = sec 6 + sec f '() = $$6(sec()tan())(6+sec( ))2 5. 1/1 points | Previous AnswersSEssCalcET2 2.4.025. Differentiate. f(z) = f '(z) = z z+ d z 2dz(z2+d)2 https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 2 of 6 ECET2e Section 2.4 21/10/2016, 02:30 6. -/1 pointsSEssCalcET2 2.4.027. Find an equation of the tangent line to the given curve at the specified point. y= x2 1 x2 + x + 1 , (1, 0) y= 7. -/2 pointsSEssCalcET2 2.4.035. If H() = sin , find H'() and H''(). H'() = H''() = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 3 of 6 ECET2e Section 2.4 21/10/2016, 02:30 8. -/2 pointsSEssCalcET2 2.4.044. Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown. (a) Find P'(2). (b) Find Q'(7). 9. -/2 pointsSEssCalcET2 2.4.048. Find equations of the tangent lines to the curve x1 x+1 that are parallel to the line x 2y = 4. y= y = (smaller y-intercept) y = (larger y-intercept) 10.2/4 points | Previous AnswersSEssCalcET2 2.4.050. A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 4 of 6 ECET2e Section 2.4 21/10/2016, 02:30 in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p). (a) What does it mean to say that f(25) = 10,000? When the price of fabric is $25/yard, 10,000 yards will be sold. When the price of fabric is $275/yard, 25 yards will be sold. When the price of fabric is $25/yard, 275 yards will be sold. There are 10,000 total yards of fabric and $275 to spend on it. There are 275 total yards of fabric and $25 to spend on it. What does it mean to say that f '(25) = 275? As the price of the fabric increases past $275/yard, the amount of fabric which will be sold is increasing at a rate of 25 yards per (dollar per yard). As the price of the fabric decreases past $25/yard, the amount of fabric which will be sold is increasing at a rate of $275 per (dollar per yard). As the price of the fabric decreases past $275/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard). As the price of the fabric decreases past $25/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard). As the price of the fabric increases past $25/yard, the amount of fabric which will be sold is decreasing at a rate of 275 yards per (dollar per yard). (b) Assuming the values in part (a), find R'(25). R'(25) = Interpret your answer. https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 5 of 6 ECET2e Section 2.4 21/10/2016, 02:30 As the price of fabric increases past $275/yard, the total revenue is increasing at $10,000 per (dollar per yard). As the price of fabric decreases past $275/yard, the total revenue is increasing at $3125 per (dollar per yard). As the price of fabric increases past $25/yard, the total revenue is increasing at $3125 per (dollar per yard). As the price of fabric increases past $25/yard, the total revenue is decreasing at $275 per (dollar per yard). As the price of fabric decreases past $25/yard, the total revenue is decreasing at $10,000 per (dollar per yard). https://www.webassign.net/web/Student/Assignment-Responses/last?dep=14686156 Page 6 of 6