If the derivative of a differentiable function is decreasing on an open interval

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

If the derivative of a differentiable function

f

is decreasing on an open interval, which of the following must be true on that interval? (a)

f\,\text{is concave up.}

(b)

f\,\text{is increasing.}

(c)

f\,\text{is concave down.}

(d)

f\,\text{has an inflection point at every } x \,\text{in the interval.}