18. C(x)=0.04x2Over what interval is each function increasing and over what interval is each function decreasing?SEE EXAMPLE 320.\begin{tabular}{|c|c|c|}\hlinex & f(x)=−0.3x2 & (x,y) \\\hline−2 & −1.2 & (−2,−1.2) \\\hline−1 & −0.3 & (−1,−0.3) \\\hline 0 & 0 & (0,0) \\\hline 1 & −0.3 & (1,−0.3) \\\hline 2 & −1.2 & (2,−1.2) \\\hline\end{tabular}
Q. 18. C(x)=0.04x2Over what interval is each function increasing and over what interval is each function decreasing?SEE EXAMPLE 320.\begin{tabular}{|c|c|c|}\hlinex & f(x)=−0.3x2 & (x,y) \\\hline−2 & −1.2 & (−2,−1.2) \\\hline−1 & −0.3 & (−1,−0.3) \\\hline 0 & 0 & (0,0) \\\hline 1 & −0.3 & (1,−0.3) \\\hline 2 & −1.2 & (2,−1.2) \\\hline\end{tabular}
Find Derivative: To determine where the function C(x)=0.04x2 is increasing or decreasing, we need to find its first derivative, C′(x), which will give us the rate of change of the function.
Calculate Derivative: Calculate the first derivative of C(x)=0.04x2 with respect to x.C′(x)=dxd(0.04x2)=0.08x
Analyze Derivative: Analyze the first derivative to determine where it is positive (function is increasing) and where it is negative (function is decreasing).Since C′(x)=0.08x, the derivative is positive when x>0 and negative when x<0.
Conclude Intervals: Conclude the intervals of increase and decrease for the function C(x). The function C(x) is increasing on the interval (0,∞) and decreasing on the interval (−∞,0).