Calculus A Chapter 4 T/F

If x=c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x-k) , where k is a constant.

False

The relative maxima of the function f are f(1) = 4 and f(3)= 10. Therefore, f has at least one minimum for some x in the interval (1, 3) .

False, function might not be continuous

The product of two increasing functions is increasing.

False, x^2

If the graph of a function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal.

False. f must also be continuous and differentiable on each interval.

If x = c is a critical number of the function f, then it is also a critical number of the function g(x)= f(x) + k, where k is a constant.

True

The graph of every cubic polynomial has precisely one point of inflection.

True

The maximum of a function that is continuous on a closed interval can occur at two different values in the interval.

True

The sum of two increasing functions is increasing.

True

If the graph of a polynomial function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal.

True. A polynomial is continuous and differentiable everywhere.

Every nth-degree polynomial has (n - 1) critical numbers.

False

If f ' (x) > 0 for all real numbers x, then f increases without bound.

False

If f '' (x) < 0 for all real numbers x, then f decreases without bound.

False

An n-th degree polynomial has at most (n-1) critical numbers.

True

If a function is continuous on a closed interval, then it must have a minimum on the interval.

True