Complete A-D please ### Understanding Increasing Functions and Concavity Here is an educational analysis of an increasing function h(t) with various properties:**b. Explanation of why h(t) is an increasing function:**To understand why the function h is increasing, identify the correct rationale from the options provided:- **A.** The height of the container is increasing at all times.- **B.** Water is being added to the container at all times.- **C.** The derivative of h is always increasing.- **D.** The value of t is always increasing.To ascertain the correct explanation, think about the relationship between the derivative of a function and its increasing nature.**c. Description of the concavity of the function h(t):**Here we need to describe the concavity of the function and identify any inflection points:- **A.** The function is concave down throughout \(0 \le t \le 10\). The function has no inflection points.- **B.** The function is concave up on \( (0, 5) \), then concave down on \( (5, 10) \). The function has an inflection point at \( t = 5 \).- **C.** The function has no concavity, then is concave down, then has no concavity, then is concave up, then has no concavity. The function has no inflection points.- **D.** The function is concave down on \( (0, 5) \), then concave up on \( (5, 10) \). The function has an inflection point at \( t = 5 \).Choose the correct description by looking for changes in concavity.**d. Determination of where the derivative of h(t) has an absolute maximum on \( [0, 10] \):**Identify where the derivative \( h' \) reaches its absolute maximum on the interval \( [0, 10] \).Choose the correct analysis from the provided options to understand these properties better and to correctly solve similar problems in future scenarios. **Description of the Problem and Solution Explanation****Title: Understanding the Depth-Time Relationship in a Variable-Shaped Container****Problem Description:**The figure on the right shows a container that is to be filled with water from the top. This particular container has a unique shape, where the horizontal cross-sections are always circular but vary in size. Water is poured into the container at a constant rate, and the container is filled in exactly 10 seconds. Let \( h(t) \) represent the depth of water in the container at time \( t \), for \( 0 \le t \le 10 \). Our goal is to determine the correct graph of the function \( y = h(t) \) for the given time interval.**Diagrams and Graph Explanation:****Container Image:**An image of the container shows it has a varying cross-sectional area with wider and narrower sections along its height.**Graphs Options:**There are four graph options provided for \( h(t) \):1. **Option A:** - The graph starts horizontally, indicating no initial increase in depth. - At some point, the graph shows an upward curve, indicating increasing depth more rapidly over time.2. **Option B:** - The graph starts with a sharp increase, then levels off towards the top, showing the depth increases quickly at first but slows down as it reaches the top.3. **Option C:** - The graph shows a gentle increase at the beginning, followed by a sharp rise towards the end, indicating depth increases slowly at first and more rapidly towards completion.4. **Option D:** - This graph shows a consistent linear increase in depth over time, indicating a constant rate of depth increase.**Correct Graph Interpretation:**To determine which graph accurately reflects \( h(t) \), consider the shape of the container. Given that water is poured at a constant rate and the container has varying cross-sectional areas, the depth-rate change won't be uniform. The correct graph will represent how depth varies in accordance with the container's changes in cross-sectional area.- In narrow sections, the depth will increase more quickly.- In wider sections, the depth will increase more slowly. Given these factors, **Option C** is likely the correct graph because it shows a slow initial increase in depth when the water fills the wider section at the bottom, and a rapid increase towards the end, reflecting the narrower section at the top

A cylindrical figure is given in which water is being poured at a constant rate and the container…

The figure to the right shows a container that is to be filled with water from the top. Assume that water is poured into the container at a constant rate and the container is filled in 10 s. Assume also that the horizontal cross sections of the container are always circles. Let h(t) be the depth of the water in the container at time t, for 0sts 10. Complete parts (a) through (d) below. a. Sketch a graph of the function y=h(t), for 0 sts 10. Choose the correct graph below. O C. O D. OB. OA. Q Q Q Q Q E O Ah O Ah C 1 -↑ Ah P