choose the correct answer. a. suppose f is continuous on an interval i and differentiable at every interior…

choose the correct answer. a. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)>0 at all interior points of i, then f is increasing on i. if f(x)<0 for all x in i, then f is decreasing on i. b. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)>0 at all interior points of i, then f is increasing or decreasing on i. c. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)<0 at all interior points of i, then f is increasing on i. if f(x)>0 for all x in i, then f is decreasing on i. d. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)<0 at all interior points of i, then f is increasing or decreasing on i.

choose the correct answer. a. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)>0 at all interior points of i, then f is increasing on i. if f(x)<0 for all x in i, then f is decreasing on i. b. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)>0 at all interior points of i, then f is increasing or decreasing on i. c. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)<0 at all interior points of i, then f is increasing on i. if f(x)>0 for all x in i, then f is decreasing on i. d. suppose f is continuous on an interval i and differentiable at every interior point of i. if f(x)<0 at all interior points of i, then f is increasing or decreasing on i.

Answer

Brief Explanations:

The first - derivative test states that if a function (y = f(x)) is continuous on an interval (I) and differentiable on the interior of (I), then: if (f^{\prime}(x)>0) for all (x) in the interior of (I), the function (f(x)) is increasing on (I); if (f^{\prime}(x)<0) for all (x) in the interior of (I), the function (f(x)) is decreasing on (I). Option A correctly states this relationship.

Answer:

A. Suppose f is continuous on an interval I and differentiable at every interior point of I. If f’(x)>0 at all interior points of I, then f is increasing on I. If f’(x)<0 for all x in I, then f is decreasing on I.