Calculus 1 Hour Exam 2 - Math 220 Fall, 2011

1.	Find g ‘ (t) given that g(t) = 5t^6 - 4t^3 + 10t + e^2 Answer: 30 t^5 - 12t^2 + 10
2.	Find dv/dt given that v = 5t^4 tan^-1 t Answer: dv/dt = 20 t^3 tan^-1 t + 5t^4 / ( 1 + t^2 )
3.	Find f ‘(x) given that f(x) = ln x / (x^3 + 4) Answer: f ‘ = [ (1/x) (x^3 + 4) - ( ln x )(3x^2) ] / (x^3 + 4)^2
4.	Find f ‘ (x) given that f (x) = sin (e^2t) Answer: f ‘ = 2 cos (e^2t) e^2t
5.	Find the slope of the line tangent to the curve x^2y^3 = 3x – 2y at the point (2,1). Answer: dy/dx = -1/14
6.	A function f(x) has the following second derivative. f‘’ (x) = ( x + 5 )^2– 4 What is the largest open interval upon which the graph of f(x) is concave down? Answer: ( -7, -3 )
7.	A particle moves along the curve y = (4/9) x^2 . As the particle passes through the point (3,4), its x-coordinate increases at the rate of 15 cm/s. How fast is the distance from the particle to the origin changing at this instant? Answer: 41 cm/s Click here to continue with this exam.

Return to "Hints and Answers to Exams"

Return to Table of Course Notes