Find all critical numbers for the function. State whether it leads to a local maximum, a local minimum, or neither. f(x)= x−8
x+5
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Local minimum at 8 Local maximum at −13; local minimum at 8 Local maximum at −13 No critical numbers; no local extrema Question 11 The rule of the derivative of a function f is given. Find the location of all local extrema. f ′
(x)=(x+5)(x+2)(x−4) Local maxima at −5 and 4 ; local minimum at −2 Local maximum at 2; local minima at 5 and −4 Local maxima at 5 and −4; local minimum at 2 Local maximum at −2; local minima at −5 and 4 The rule of the derivative of a function f is given. Find the location of all points of inflection of the function f. f ′
(x)=(x 2
−4)(x+3) (2,−3 −2,−3,2 -1 −2.53,0.53 Question 13 Solve the problem. If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p=37− 12
x
​
. How many bolts must be sold to maximize revenue? 222 bolts 222 thousand bolts 444 thousand bolts 444 bolts Solve the problem. When an object is dropped straight down, the distance in feet that it falls in t seconds is given by s(t)=−16t 2
, where negative distance (or velocity) indicates downward motion. Find the velocity and acceleration at t=8. Velocity =−256ft/sec; acceleration =0ft/sec 2
Velocity =−32ft/sec; acceleration =−256ft/sec 2
Velocity =−256ft/sec; acceleration =−32ft/sec 2
Velocity =−32ft/sec; acceleration =0ft/sec 2
Question 15 Solve the problem. Because of material shortages, it is increasingly expensive to produce 6.0 L diesel engines. In fact, the profit in millions of dollars from producing x hundred thousand engines is approximated by P(x)=−x 3
+27x 2
+15x−52 where 0≤x≤20. Find the point of diminishing returns. (9.00,1415.00) (6.75,1541.00) (9.00,1541.00) (9.00,137.00)