MTH 235 Lecture 10: Note 11 сент. 2019 г. (2)

1 2. (a) Find the tangent line to the graph of s(2)=x+ when r = 1. (b) Find the derivative of p(x) = (ln(5.c) + )(2-3V ). (c) Find the derivative of j(x) = 60(2*+52) (d) Find the derivative of k(2) = (e) The following table gives some values for f(x), f'(x), g(x), and g'(x). | f(x) | 3|1|2|2 f'(x) | 1 46 | 4 g(1) 0-183 () -2 0 4-1 • Let h(x) = f(t)g(2). Find h' (6). • Let r(x) = f(g(x)). Find /'6).

So when I calculated I got that the bounds for u were -3/9<u<0 and 0<v<8/9. How is it 0 to 1 for both? Thank you. This is in the change of variables example

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed