Question

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) f(x) = x2*49 intercept (x, y) = ( 0,0 relative minimum (x, y) = ( 0,0 x relative maximum (x, y) = DNE point of inflection (x, y) = 0.0 Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations differ by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results. f(x) = x3 - 9.9x2 + 32.39x - 35.061 Newton's method: Graphing Utility: (smallest value) x = X = X (largest value) The range R of a projectile is shown below, where vo is the initial velocity in feet per second and is the angle of elevation. RE VO2 (sin 20) 32 Use differentials to approximate the change in the range when Vo = 2700 feet per second and is changed from 10° to 8º. (Round your answer to the nearest whole number.) 15280 X ft

Answer 1

23 2 take ya =) d=0 2 = 0, f(x) = x² (n²-147) f(n) = n²-49 ²-492 f(n) = aor (x²+147) m2 - 49) 3 For & intercept, (0,0) is the only intercept. solve f'(a) =0 for critical point. =) and Maoviny at d=0 fino=0 f'img co and left side of d=0 on Right side of n=0 That means sign of f'rm) is same on both side of n=0. a inflection point. Vint left side of na m= Ving, f'(my co on Right side of de = Vint, f'im) o So, =viyt relative minimum. at na viui, y = -18.187 f'(a) co so, do is at na f'(o)=0 ག da

= - 12.124 - 0 on Vinta <o so at dr-ving if la left of dar -Vint, f'm so on Right of non f'm) - Viny relative maximum y = -18. 187 Point. Therefore, minimum (Jint, +18, 187) relative maximum (-vint, - 18. 187) point of inflection is cool vertical asymptote relative 2² - - 49=0 = =-7 or n=7 vertical asymptote (by taking denominator equal to Zero heart Here, degree of denominator less than degree of nume sator. exist horizontal asymptote. So There ло 3 = (2-4a) * +4am x²_49 ²-49 Here slant 2 vs asymptote y = 490 in Cox, Viny) U (Vint, oo) f(n) > o =) frm) is increasin (-147 ) u (-7, -1) U (T, VIHT), fino -> fom is intal.decoensing. -

50 (12.124, 18.187) (0.0) -100 -50 0 50 100 (-12.124, -18.187) -50