Question

solar panel power output the graph of the function f shown in the accompanying figure gives the average fixed solar panel power output over a 15 - hr period on a typical day. determine the interval(s) where f is increasing, the interval(s) where f is constant, and the interval(s) where f is decreasing. here, t = 0 corresponds to 5 a.m. (enter your answers using interval notation. if an answer does not exist, enter dne.)

Explanation:

Step1: Analyze the graph for increasing intervals

The graph shows that the function \( f \) (solar panel power output) is increasing when the slope of the graph is positive. Looking at the \( t \)-axis (time), from \( t = 0\) (5 a.m.) to \( t = 10\) (3 p.m.), the \( y \)-values (solar panel operating capacity) are rising. So the interval where \( f \) is increasing is \([0,10]\).

Step2: Analyze the graph for decreasing intervals

The function \( f \) is decreasing when the slope of the graph is negative. From \( t = 10\) (3 p.m.) to \( t = 15\) (8 p.m.), the \( y \)-values are falling. So the interval where \( f \) is decreasing is \([10,15]\).

Answer:

The function \( f \) is increasing on the interval \([0,10]\) and decreasing on the interval \([10,15]\).