DIFFERENTIAL CALC

Question 1

The point where the concavity of a
curve changes is called the

A. inflection point
B. tangent point
C. maximum point
D. minimum point

Answer 1

A. inflection point

Maximum - a point at which a
function’s value is greatest. If the
value is greater than or equal to all
other function values, it is an absolute
maximum. If it is merely greater than
any nearby point, it is a relative or
local maximum.

Minimum - a point at which the value of a function is less than or equal is less than or equal to value at any
nearby point (local minimum) or at
any point (absolute minimum).

Tangent point - A point where a line touches another curve on that single point

Question 2

What is also known as the Second
Fundamental Theorem of Calculus

A. Newton-Leibniz axiom
B. Von Neumann-Bernays-Gödel axioms
C. Noethers second theorem
D. Dunford-Schwartz theorem

Answer 2

A. Newton-Leibniz axiom

Question 3

A fractional derivative of order 1/2.

A. Semi derivative
B. Sub derivative
C. Inverse derivative
D. Anti derivative

Answer 3

A. Semi derivative

Question 4

If a and b are positive numbers, find the
x coordinate which gives the absolute
maximum value of f(x)= x(1 -X) on the
interval [0, 1].

A. a/a+2b
B. 2a/a+b
C. b/a+b
D. a/a+b

Answer 4

D. a/a+b

Question 5

What is the domain of the function
defined by f(x) = (x^2)/√x?

A. x < 0
B. any real number
C. x ≠ 0
D. x > 0

Answer 5

D. x > 0

Since we have √x in the denominator, x
must not be equal to 0 (so that the
function will not become undefined) and must not be negative (since x is inside a square root). Thus, the domain of the function are all real numbers greater than 0.
Thus, the answer is x > 0.

Question 6

If the hypotenuse of a right triangle is
known, what is the ratio of the base and the altitude of the right triangle when its area is maximum?

A. 1:4
B. 1:1
C. 1:3
D. 1:2

Answer 6

B. 1:1

In order to maximize the area, the base
and altitude must be equal. Thus, the
ratio of the base and altitude is 1:1.