MATH 1271 Lecture 4: 4.1- Extreme Values

PLE CHOICE. Choose the one alternative that best completes the statement or answers the question. he largest open interval where the function is changing as requested. F( 1) Increasing f(x)= x2+1 1) d the absolute extreme values of the function on the interval. 2)f(x)=ln(x + 2) +x1sxz5 ,A) Minimum value is 2) In 4 +흘 atx=2;maximum value is In 7 atxs3 B) Minimum value is -1 at x--1; maximum value is In 7 atx 5 C)Minimum value is ln 4 + at x = 2; maximum value is In 3-1 at x=1. D) Minimum value is In 3+1 at x=1; maximum value is 1n7+5atx-3 Determine all critical points for the function. 3)y-2x2-64F 3) A)x=4 C) x 0 and x 4 B)x=0 D) x=0, x " 4, and x--4 Find the absolute extreme values of the function on the interval 4)F(x)- 0.5sxs4 4) A) absolute maximum is at x = ; absolute minimum is-12 at- B)absolute maximum is-atx absolute minimumis-12at C)absolute maximum is atx.4;absolute minimum is-12atx D) absolute maximum is - 16 at x - 4, absolute minimum is -12at x- 2 16 16 Find the formula for df-l/dx. 5) f(x) = x73 5) C A) x37 B) -47 D) x47 B-1

Find the largest open interval where the function is changing as requested 1) Increasing f)2. 1) x2+1 Find the absolute extreme values of the function on the interval. 2) 2) fo)-Ink + 2).1sxs5 A)Minimum value is 1n 4·를 atx.2;maximum value isln7.rx-5 B)Minimum value is-1 at x=-1; maximum value is 1n7-sat x=5 C) Minimum value is In 4 atx -2, maximum value is in 3+1 at x-1 D) Minimum value is In3+ 1atx 1; maximum value is In 7 atx-5 Determine all critical points for the function. 3)y=2x2-64F A) x4 3) B) x=0 D) x=0,x=4,and x-4 x " 0 and x = 4 Find the absolute extreme values of the function on the interval. 4)F(x) =-_, 0.5sxs4 A) absolute maximum is an« ; absolute minimum is-12 ahe4 B) absolute maximum is-at x = ; absolute minimum is-12 at…4 C) absolute maximum is-at x-4; absolute minimum is -12 at x 16 2 16 2 16 D)absolute maximum s- at x . 4; absolute minimum is-12at… 16 2 Find the formula for df-1/dx. 5) f(x)-x73 A) x37 5) 243 D) x47 B) B-1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the quest Find the largest open interval where the function is changing as requested. -1- x2+1 1) Increasing f(x)= Find the absolute extreme values of the function on the interval. 2) fo) Ink+2) 1sx5 A) Minimum value is In 4 + 1 at x-2; maximium value is ln 7 + 즐 at x-5 B) Minimum value is-1 at x =-1; maximum value is In 7 + 즐 at x-5 d) Minimum value is In 4 + at x =2;maximum value is In 3 + 1 atx.1 D)Minimum value is In 3 + 1 atx-1; maximum value is In 7 tx.5 Determine all critical points for the function. 3)y=2x2-64E A)x=4 c) x = 0 and x = 4 D) x=0,x24, and x =-4 Find the absolute extreme values of the function on the interval. 4)F(x)-- 0.5sxs4 A) absolute maximum is B) absolute maximum is- C) absolute maximum is- ; absolute minimum is-12 atx4 2 at x= 16 at x absolute minimum is-12 at x-4 16 at x = 4; absolute minimum is-12 at x 16 nimum is -12 atx- 16 Find the formula for df-1/dx. 5) f(x) x7/3 A) x37 B) 클x-4/7 D) x4/7