In Exercises 65-68, use the graph of f\' to (a) identify the interval(s) on whic
ID: 3342769 • Letter: I
Question
In Exercises 65-68, use the graph of f' to (a) identify the interval(s) on which f is increasing or decreasing, and (b) estimate the value(s) of x at which f has a relative maximum or minimum. In Exercises 3-8, use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. y = x3/4 - 3x Power The formula for the power output P of a battery is P = VI - RI2, where V is the electromotive force in volts, R is the resistance in ohms, and I is the current in amperes. Find the current that corresponds to a maximum value of P in a battery for which V = 12 volts and R = 0.5 ohm. Assume that a 15-ampere fuse bounds the output in the interval 0 I 15. Could the power output be increased by replacing the 15-ampere fuse with a 20-ampere fuse? Explain.Explanation / Answer
66) a)from graph of f' we can say f is increasing in (- infi,0) union ( 1, + infinity) and decreasing in(0,1)
b)rel minima at x=0 and maxima at x=1
5)From graph it increases in (-infi , -2) union ( 2,infi) abd decreases in (-2,2)
f'(x)=3/4 x^2 -3 this is >0 in (-infi , -2) union( 2,infi)and < 0 in (-2,2)
soit matches the result from graph
61)P=12I -0.5 I^2 for P max dp/dI=0 and d2p/di2 <0
so 12 -2*0.5 I=0 => I =12 A........ and d2p/di2=-i=-12<0.................So max P is at I=12 Amperes
No by replacing fuse we cannot because we have a maxima at I=12 itself