Question

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#2(b)) What types of functions are f(x) = e" and g(x) = x". Compare the differentiation formulas for f and 9 # 3,4,6,11,14,19.21) Differentiate the function: # 3) f(x) = 186.5 # 4) f(1) = 30 # 6) (t) = {- 36 +t #11) G(x) = VI - 2* # 14) R(r) = YTO #19) y = +*+47 +3 # 21) v = # 25) Find the equation of the tangent line and normal line to the curve y = x + em at the point (0,1). # 38) Find the first and second derivatives of the function G(r) = r + r. # 41) The equation of motion of a particle is s = + - 3t, where s is in meters and t is in seconds. Find (a) the velocity and acceleration as functions of t, (b) the acceleration after 2 s, and (c) the acceleration when the velocity is 0. # 43) On what interval is the function f(1) = 1 + ef - 3r increasing? # 44) On what interval is the function f(r) = r - 4.x2 + 5.6 concave upward? # 45) Find the points on the curve y = 2.x3 + 3.rº – 12.c + 1 where the tangent line is horizontal

Answer 1

f(x) = 960 = x variable Here function fin) = (constant constant while groo- (variable) For derivative of fox) We use the formula el fond) = a (eta eta bere e function as it is and derivative of power function for is also known as / exponefiat function For gir) = x , we use the desihative as formula = neni it. Power less then I and & multiply by old bower. gon) = n is also known as polynomial function. frow = 186.5 constant function fon) = 30 again consten functian