Question

70 60 50 40 30 20 10 -19 10 20 30 40 50 60 You are a lifeguard and spot a drowning child 60 meters along the shore and 70 meters from the shore to the child. You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of 3 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should you run before jumping into the water in order to save the child? Round your answer to three decimal places 59.5 3x - 10 6x2-2x + 15 Find all critical values for f (x) - The critical values occur at x- (20-15sqrt(2)/6,-(3 15sqiPreview. (Enter your answers separated by commas) Given the function f(x) -" Determine the open interval(s) where the functiorn is concave up (-0.29289321,00)Preview Determine the open interval(s) where the function is concave down Preview , (-1.70710678,-0.2928932 Determine any points of inflection. (-0.29289321,0.0477545! List the x-coordinates of the critical values (enter DNE if none) DNE List the x-coordinates of the inflection points (enter DNE if none) DNE List the intervals over which the function is increasing or decreasing (use DNE for any empty intervals) Increasing on DNE Preview Decreasing on1/5 Preview List the intervals over which the function is concave up or concave down (use DNE for any empty intervals) Concave up on 1/5 Preview Concave down on Preview DNE Consider the function r(24160 15. Differentiate r and use the derivative to determine each of the following All intervals on which r is increasing. If there are more than one intervals, separate them by a comma. Use open intervals and exact values. r increases on: 10,15] 丼 Preview All intervals on which r is decreasing. If there are more than one intervals, separate them by a comma. Use open intervals and exact values. r decreases on: [0,15] Preview The value(s) of z at which r has a relative maximum. If there are more than one solutions, separate r has relative maximum(s) at z te them by a comma. Use exact values. Preview The value(s) of r at which r has a relative minimum. If there are more than one solutions, separate them by a comma. Use exact values. r has relative minimum(s) at 2 Preview Find the maximum and minimum values of the function g(9) 2θ-4 sin(θ) on the interval 0 2 Minimum value pi/3+2pi Preview Maximum value 0 Preview

Answer 1

O b A and ther swiuu from A to c Total +me taken, 60-х 3 J4900422 1.1 f(x): 8 o23 "X (1.1) Juq00t2 3 어: 27.588 32-412m distance along the Aheres, 60- C2R 224 ls) (3)-(37-10) (122-2) 6で224 is) 2 f(X). ズ コ 6거2-2ズ+15 186+45 3622 26-21822+12 2 요 critica! p sint, 41»: o or D.NE -1 gT+ 1202+ 2s-o -120 t Ji440+180-120t 902 (20152 36 2 C18) 3 6 f'(x)70-) C-oo,-.Fo지0678) U (-0.29 28932,00) com carve ups ', pend url intteckons(-は0지。698,-0.2928132) intteetion> (1021 0633, - .92832)