6.Derivatives Quiz

What is the definition of a maximum value of a function f in interval I?

• f(c) is equal to f(x) for all x in I

• f(c) is greater than f(x) for some x in I

• f(c) is less than f(x) for all x in I

• f(c) is greater than f(x) for all x in I

When does a point c in interval I become a point of local maxima?

• f'(x) is negative at every point close to and to the right of c, and f'(x) is positive at every point close to and to the left of c

• f'(x) is positive at every point close to and to the right of c, and f'(x) is negative at every point close to and to the left of c

• f'(x) is negative at every point close to and to the left of c, and f'(x) is positive at every point close to and to the right of c

• f'(x) is positive at every point close to and to the left of c, and f'(x) is negative at every point close to and to the right of c

What is the condition for a point c in interval I to become a point of local minima?

• f'(x) is negative at every point close to and to the right of c, and f'(x) is positive at every point close to and to the left of c

• f'(x) is positive at every point close to and to the right of c, and f'(x) is negative at every point close to and to the left of c

• f'(x) is negative at every point close to and to the left of c, and f'(x) is positive at every point close to and to the right of c

• f'(x) is positive at every point close to and to the left of c, and f'(x) is negative at every point close to and to the right of c

What is the definition of a minimum value of a function f in interval I?

• f(c) is less than f(x) for all x in I

• f(c) is less than f(x) for some x in I

• f(c) is equal to f(x) for all x in I

• f(c) is greater than f(x) for all x in I

When does a point c in interval I become a point of local inflexion?

• f'(x) is positive at every point close to and to the right of c, and f'(x) is negative at every point close to and to the left of c

• f'(x) is negative at every point close to and to the left of c, and f'(x) is positive at every point close to and to the right of c

• f'(x) is positive at every point close to and to the left of c, and f'(x) is negative at every point close to and to the right of c

• f'(x) does not change sign as x increases through c

What is the condition for a point c in interval I to become a point of extreme value?

• f(c) is greater than f(x) for all x in I

• f(c) is equal to f(x) for all x in I

• f(c) is either a maximum value or a minimum value of f in I

• f(c) is less than f(x) for all x in I

What is the number called when f has a maximum value in interval I?

• f'(c)

• f(c)

• f'(x)

• f(x)

What is the number called when f has a minimum value in interval I?

• f(c)

• f(x)

• f'(x)

• f'(c)

What is the number called when f has an extreme value in interval I?

• f(c)

• f(x)

• f'(c)

• f'(x)

What is the point called when f has an extreme value in interval I?

• c

• x

• f

• f'