Chapter 4, Problem 5CRQ

(a)

To determine

To fill: The condition for which the graph of function is increasing for differentiable function f is concave upward on an interval I

(b)

To determine

To fill: The condition for f has a second derivative and the graph of the f is concave upward on interval I.

(c)

To determine

To fill: If the graph of a continuous function f has a tangent line at $P\left(c,f\left(c\right)\right)$ and the graph of the f changes ________ at P, then P is called an inflection point of f

(d)

To determine

To fill: Suppose f has a second derivative on an interval $\left(a,b\right)$, containing a critical number c of f. If $f^{″}\left(c\right)<0$, then f has a/an ________ at c. If $f^{″}\left(c\right)=0$, then f may or may not have a/an __________ at c.