f(x)=1/3 *x³-2x
f¹(x)=1/3 *3x²-2=x²-2
Тангенс угла наклона касательной к положительному направлению оси ОХ = значению производной в точке касания.Тогда
tg135⁰=x₀²-2, где х₀-абсцисса точки касания
tg135⁰=tg(180⁰-45⁰)= -tg45⁰= -1
x₀²-2=-1, x₀²-1=0, (x₀-1)(x₀+1)=0,
x₀=1 или x₀=-1
f(x₀)=f(1)=1/3 *1-2*1=1/3-2=-5/3
f(-1)=1/3 *(-1)³-2*(-1)=-1/3+2=5/3
Координаты точек: (1; -5/3) и (-1; 5/3).
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