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Problem Let F F F F ′ ( x ) = ∣ x − 1 ∣ F'(x)=|x-1| F ′ ( x ) = ∣ x − 1∣ F ( 0 ) = 0 F(0)=0 F ( 0 ) = 0 F ( x ) F(x) F ( x ) x x x F ( x ) = { x − x 2 2 , x ≤ 1 , ( x − 1 ) 2 2 , x ≥ 1. \displaystyle F(x)=\begin{cases}x-\dfrac{x^{2}}{2}, & x\le 1,\\ \dfrac{(x-1)^{2}}{2}, & x\ge 1.\end{cases} F ( x ) = ⎩ ⎨ ⎧ x − 2 x 2 , 2 ( x − 1 ) 2 , x ≤ 1 , x ≥ 1. F ( x ) = { x − x 2 2 , x ≤ 1 , ( x − 1 ) 2 2 + 1 2 , x ≥ 1. \displaystyle F(x)=\begin{cases}x-\dfrac{x^{2}}{2}, & x\le 1,\\ \dfrac{(x-1)^{2}}{2}+\dfrac12, & x\ge 1.\end{cases} F ( x ) = ⎩ ⎨ ⎧ x − 2 x 2 , 2 ( x − 1 ) 2 + 2 1 , x ≤ 1 , x ≥ 1. F ( x ) = ( x − 1 ) 2 2 − 1 2 \displaystyle F(x)=\dfrac{(x-1)^{2}}{2}-\dfrac12 F ( x ) = 2 ( x − 1 ) 2 − 2 1 F ( x ) = { x 2 2 − x , x ≤ 1 , ( x − 1 ) 2 2 , x ≥ 1. \displaystyle F(x)=\begin{cases}\dfrac{x^{2}}{2}-x, & x\le 1,\\ \dfrac{(x-1)^{2}}{2}, & x\ge 1.\end{cases} F ( x ) = ⎩ ⎨ ⎧ 2 x 2 − x , 2 ( x − 1 ) 2 , x ≤ 1 , x ≥ 1. Browse the problem library