Local Minimum - Calculus - Solved Exam, Exams of Calculus

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MATH 105 Final Exam Review II 1. Consider the function f(z) = 25 — 22° on the interval [ 2,2). (a) Find the exact 2- and y-coordinates of any and all local extrema and classify each as a local maximum or local minimum. Fired 4- Gods, leat : (2 60) Ud - ¢ a 3 iS legal may 1 f= ox - bx NON A £(-2\> bo (ocal wax » ( 2,48) =< _ tt = O= Oi (1 eb ata fas 0 fecal mms Chi = X=0, K=/ £2) = 46 (b) Find the exact x- and y-coordinates of any: and all global extrema and classify each asa global maximum. or global minimum. From the 3 ~ coord haks Th rt (a), we sea that ut have globo ma > (-2, 80) 4 label mm: -C 1-1) (c) Find the exact x-coordinate(s) of any and all inflection points £'%(x) = 2%»! ~12X jw Gre [x =O, X= 4 | O = 6x(Sx* +2) Foe dn “? bia ge + ° - 3 t 3 = X=o, X= JE Ais J 2. You are standing on the very top of a 20-foot ladder which is leaning against the side of your house. Suddenly, the base of the ladder begins to slip backward away from the house at a rate of 3 feet per second, causing the top of the ladder (and you) to slide downward along the wall. When you are stil! 12 feet above ground, at what rate is your height above the ground changing? twant : 4 ‘@) Kuew:. x "(£) Retake x) ad yLQ 2 2072 (xe) + (gh) 3 “0 Tate 4fde of both stoles: O= 2XQ-xX® + ayy). Plug nm and solve When 3F a, O= 2 te- G3) 4 2° i2-9'&) we have 20” - r€ = eit oO AG t2Ay (t) =) 44 us [= 4 €/s| ot this ~ women. S x= le.