If the first derivative of a function is a constant, then the function is
Asinusoidal
Bexponential
Clinear
Dquadratic
Mathematics · Question Bank
Differential Calculus
66 questions · page 2 of 4. Answer in your head first, then check the solution.
A function f(x) is said to be an even function if its graph is symmetric with respect to
Athe x-axis
Bthe y-axis
Cthe origin
Dboth axes
The notation f’(x) was invented by
ALeibniz
BNewton
CWallis
DLagrange
If a function f(x) is concave downward on the interval (1,10), then f(8) and f(3)
Amay be true
Bcannot be true
Cmust be true
Dis never true
If a tangent to a curve y = f(x) is horizontal at x = a, then f’(a) is
Apositive
Bnegative
Czero
Dinfinity
For a function y = f(x), if f”(x) = -f(x), then the function is
Alogarithmic
Bexponential
Ctranscendental
Dsinusoidal
The derivative of an increasing function f(x) must be
Astrictly positive
Balways positive
Cnon-negative
Dnegative
At the maximum point, the value of the 2nd derivative of a function is
Apositive
Bnegative
Czero
Dinfinite
At the inflection point, the value of y” is
Azero
Bpositive
Cnegative
Dunity
The function y = f(x) has a maximum value of x = 2 if f’(2) = 0 and f”(2) is
Aequal to zero
Bless than zero
Cgreater than zero
Dunity
At the maximum point, the tangent line is
Aslanting upward
Boblique
Chorizontal
Dvertical
Find the minimum distance from the point \((4,2)\) to the parabola \(y^2=8x\).
A\(4\sqrt{3}\)
B\(2\sqrt{2}\)
C\(\sqrt{3}\)
D\(2\sqrt{3}\)
The sum of two positive numbers is 50. What are the numbers if their product is to be the largest possible.
A24 & 26
B28 & 22
C25 & 25
D20 & 30
A triangle has variable sides x,y,z subject to the constraint such that the perimeter is fixed to 18 cm. What is the maximum possible area for the triangle?
A\(15.59 \text{ cm}^2\)
B\(18.71 \text{ cm}^2\)
C\(17.15 \text{ cm}^2\)
D\(14.03 \text{ cm}^2\)
A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?
A\(25 \text{ m} \times 25 \text{ m}\)
B\(15 \text{ m} \times 35 \text{ m}\)
C\(20 \text{ m} \times 30 \text{ m}\)
D\(22.5 \text{ m} \times 27.5 \text{ m}\)
Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108 cu. inches in square inches.
A125.50
B127.50
C129.50
D123.50
A box is to be constructed from a piece of zinc 20 sq.in by cutting equal squares from each corner and turning up the zinc to form the side. What is the volume of the largest box that can be so constructed?
A599.95 cu in.
B592.59 cu in.
C579.50 cu in.
D622.49 cu in.
A poster is to contain 300 (cm square) of printed matter with margins of 10 cm at the top and bottom and 5 cm at each side. Find the overall dimensions if the total area of the poster is minimum.
A27.76 cm, 47.8 cm
B20.45 cm, 35.6 cm
C22.24 cm, 44.5 cm
D25.55 cm, 46.7 cm
A norman window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter?
A1
B\(1/2\)
C2
D\(2/3\)
Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu. m to obtain minimum surface area.
A1.22
B1.64
C2.44
D2.68