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(6pts.) Find the absolute maximum and minimum values of f(x) = x3 + 3x2-2 on the

ID: 2887515 • Letter: #

Question

(6pts.) Find the absolute maximum and minimum values of f(x) = x3 + 3x2-2 on the closed interval [-1,1]. (6pts.) A particle moves along the x-axis with an acceleration given by a(t) 6t + 2, where t is measured in seconds and s (position) is measured in meters. If the initial position is given by s(0) ; 3 and the initial velocity is given by v(O)4 then find the position of the particle at t seconds. (5pts.) Find two positive numbers such that their product is equal to 100 and their sum is minimal.

Explanation / Answer

f(x) = x3 + 3x2-2

f '(x) = 3x2+ 6x

Critical number, f '(x) = 0

3x2+ 6x =0

3x( x+2) =0

x =0 , x+2 =0

x = 0 , x =-2

f(-1) = -1 + 3 -2 = 0

f(0) = -2

f(1) = 1 +3 -2 = 2

Absolute maxima = 2 at x=1

Absolute minima = -2 at x=0