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 Problem: maximum and minimum value of y=4x^3+19x^2-14x+3 [ Calculator, Method and examples ]Solution:Your problem -> maximum and minimum value of y=4x^3+19x^2-14x+3Here, y=4x^3+19x^2-14x+3:. (dy)/(dx)=d/(dx)(4x^3+19x^2-14x+3)=d/(dx)(4x^3)+d/(dx)(19x^2)-d/(dx)(14x)+d/(dx)(3)=12x^2+38x-14+0=12x^2+38x-14For stationary values, (dy)/(dx)=0=>12x^2+38x-14=0=>2(6x^2+19x-7)=0=>2(6x^2-2x+21x-7)=0=>2(2x(3x-1)+7(3x-1))=0=>2(2x+7)(3x-1)=0=>2x+7=0" or "3x-1=0=>2x=-7" or "3x=1=>x=-7/2" or "x=1/3:.At x=-7/2 and x=1/3 we get stationary values.Now, (d^2y)/(dx^2)==12x^2+38x-14d/(dx)(12x^2+38x-14)=d/(dx)(12x^2)+d/(dx)(38x)-d/(dx)(14)=24x+38-0=24x+38((d^2y)/(dx^2))_(x=-7/2)=24*(-7/2)+38=-84+38=-46 (negative):. At x=-7/2 the function is maximum((d^2y)/(dx^2))_(x=1/3)=24*(1/3)+38=8+38=46 (positive):. At x=1/3 the function is minimumNow, y=4x^3+19x^2-14x+3"putting " x=-7/2y_(max)=4*(-7/2)^3+19*(-7/2)^2-14*(-7/2)+3=-343/2+931/4+49+3=453/4"putting " x=1/3y_(min)=4*(1/3)^3+19*(1/3)^2-14*(1/3)+3=4/27+19/9-14/3+3=16/27

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