Since {{MATH_219}}, it follows that the function {{MATH_220}} is increasing on the interval {{MATH_221}} and decreasing on the interval {{MATH_222}} Since the function {{MATH_223}}, the derivative of {{MATH_224}}, is increasing on {{MATH_225}}, {{MATH_226}} is concave up on the interval {{MATH_227}} Since {{MATH_228}} is constant on the interval {{MATH_229}}, {{MATH_230}} is linear on {{MATH_231}}.