MAE101 - Test 1 UPDATED Exam Questions and CORRECT Answers

MAE101 - Test 1 UPDATED Exam
Questions and CORRECT Answers
The displacement (in feet) of a certain particle moving in a straight line is given by s = t3+2t
where t is measured in seconds. Find the average velocity over the interval [1.5, 2].
a. None of the other choices is correct
b. 22.5 feet per second
c. 8.75 feet per second
d. 14 feet per second

e. 11.25 feet per second - CORRECT ANSWER - The correct answer is: 11.25 feet per second


Find an equation of the tangent line to the parabola y =x2 at (-2, 4).
a. y = -4x -12
b. y = -4x - 4
c. y = -4x

d. y = -4x +4 - CORRECT ANSWER - The correct answer is: y = -4x - 4


Find an equation of the tangent line to the curve 4x2+3y2=7 at the point (1, 1).
a. y = -1.33x + 2.33
b. y= -x + 2.33
c. y = -2x +4.33

d. y = -1.33 x -2.33 - CORRECT ANSWER - The correct answer is: y = -1.33x + 2.33


Find a linear approximation for f(x)=x3 at x = 1.
a. 3x-2
b. 2x+1
c. 3x+2
d. 2x-1

,e. None of the other choices is correct - CORRECT ANSWER - The correct answer is: 3x-2


Estimate the absolute minimum value of the function y = x3-6x+3 on the interval [0 , 10].Round
your answer to two decimal places
a. -2.66
b. -1,56
c. 2.56
d. -3.78

e. -2 - CORRECT ANSWER - The correct answer is: -2.66


Find the minimum of the product of two numbers with the property that the first minus 5 times
the second is 7.
a. -2.45
b. -3
c. None of the other choices is correct
d. -7
e. 0

f. -4.25 - CORRECT ANSWER - The correct answer is: -2.45


Use Newton's method with the specified initial approximation x1 to find x3, the third
approximation to the root of the given equation.


x3-2x+1=0, x1=2


(Give your answer to 4 decimal places)
a. 1.2105
b. 0.9657
c. 1.6324
d. 1.3425

,e. None of the other choices is correct - CORRECT ANSWER - The correct answer is: 1.2105



Find ff ''(x)=6x+3x2 - CORRECT ANSWER - The correct answer is: x^3+(x^4/4)+Cx+D


From the graph of y = f(x), how do we obtain the graph of y = f(x+3) -2?
a. Shift to the right by 3, and then shift up by 2
b. Shift to the left by 3, and then shift down by 2
c. Shift to the left by 2, and then shift down by 3
d. Shift to the right by 2, and then shift up by 3

e. None of the other choices is correct - CORRECT ANSWER - The correct answer is: Shift
to the left by 3, and then shift down by 2


Simplify [f(x+h)-f(x)] / h forf(x) = -3x2 +2
a. -6x+2h
b. -6x
c. None of the other choices is correct
d. -6x-3h+2

e. -6x-3h - CORRECT ANSWER - The correct answer is: -6x-3h


Find f ' in terms of g '.f(x) = [g(x)]2
a. f'(x)=2g(x)(g'(x)+x)
b. f'(x)=x[g'(x)]
c. f'(x)=2g(x)
d. None of the other choices is correct

e. f'(x)=2g(x)g'(x) - CORRECT ANSWER - The correct answer is: f'(x)=2g(x)g'(x)


Find the slope of the tangent line to the curvey2x+x3y = 6at the point (1, 2).
a. None of the other choices is correct

, b. 10/7
c. -10/7
d. 2

e. -2 - CORRECT ANSWER - The correct answer is: -2


Let x2+y3=9. Assume that dx/dt = -1, find dy/dt when y = 2.
a. 1/6; -1/6
b. 6
c. 4
d. -1/4; 1/4

e. None of the other choices is correct - CORRECT ANSWER - The correct answer is: 1/6; -
1/6


Find the absolute maximum and minimum values of the functionf(x) = x4 - x3 - (1/2)x2on the
interval [0, 2].
a. Absolute max = 6, absolute min = 0
b. Absolute max = 4, absolute min = -1/2
c. Absolute max = 6, absolute min = -1/2
d. Absolute max = 4, absolute min = 0

e. None of the other choices is correct - CORRECT ANSWER - The correct answer is:
Absolute max = 6, absolute min = -1/2


Find two positive numbers whose product is 196 and whose sum is a minimum.
a. 7; 28
b. 4; 49
c. 6; 24
d. 2; 98

e. none of these - CORRECT ANSWER - The correct answer is: none of these