Goal is to sketch the curve for f(x) defined as follows (NOTE: the implied domain is...

 

Transcribed Image Text:

Goal is to sketch the curve for f(x) defined as follows (NOTE: the implied domain is (x > 0} ] a) Find the first derivative f(x), and use this to determine all critical points. b) Find regions where increasing and regions where decreasing. Use this to classify each critical point as a relative maximum, relative minimum, or neither. C) Find the second derivative f'(x) and determine where this is zero. Use this to classify regions of concavity and identify any inflection points. [Note the limit at infinity is zero, leading to a horizontal asymptote of y-0 along the positive x-axis. ] d) Sketch the curve QUESTION 22 antiderivative problem Consider a moving particle whose acceleration is given by the following function { a(t) = t - 3+ sin t } a) Find the velocity function vt) given that the initial velocity is v_0 = 5. b) Find the position function rt) given that the initial position is r_0 = 10. Goal is to sketch the curve for f(x) defined as follows (NOTE: the implied domain is (x > 0} ] a) Find the first derivative f(x), and use this to determine all critical points. b) Find regions where increasing and regions where decreasing. Use this to classify each critical point as a relative maximum, relative minimum, or neither. C) Find the second derivative f'(x) and determine where this is zero. Use this to classify regions of concavity and identify any inflection points. [Note the limit at infinity is zero, leading to a horizontal asymptote of y-0 along the positive x-axis. ] d) Sketch the curve QUESTION 22 antiderivative problem Consider a moving particle whose acceleration is given by the following function { a(t) = t - 3+ sin t } a) Find the velocity function vt) given that the initial velocity is v_0 = 5. b) Find the position function rt) given that the initial position is r_0 = 10.