Question

Canvas Question 6 2 pts The graph of y=f(a) is shown below. y = f(x) 1 2 3 4 5 6 8 9 10 For which interval, (a, b), and a value, 2=c, can we apply the Mean Value Theorem and conclude that f(b)-f(a) b-a f(c) = (2,5), f'(4) = -1 15,7), f'(6) = -1 17,9), f'(8) = 0 [0,3), f'(2) = 1 Question 7 2 pts Suppose the width of a rectangle increases by 1/2 meters per second while the area of the rectangle remains constant at 100 square meters. What is the rate of change of the perimeter of the rectangle when the width is 5 meters? MacBook Pro

Answer 1

Rate of increase of width of rectangle dw = 2 m/s Area of rectangle. A = 100 m2 (constan) lw=100 l = 100 Now Perimeter P Rectangle P= 21+w) 52 (100+w) Rate of change perimeter avec ) ole = 2 (100+)) {+) =1-10 when width, W = 5m then d p = 1 - 100 =14 =-3 mis

The function is continuous [5,77 and is differentiable (5,7). so mean value theosem is on interval on interval applicable on (517) Now f(s)=1 417) = 0 f'(6) = f(7) - f(s) 7-5 + 2 - = -2 ... f' (6) =- Ans. [5,77. f'(6)=