设函数f（x）=e^x-k/2（x）^2-x若x≥0f（x）≥1恒成立求k的取值

Question

设函数f（x）=e^x-k/2（x）^2-x 若x≥0 f（x）≥1 恒成立 求k的取值

Answer 1

f（x）=e^x-k/2*x²-xx≥0,f（x）≥1,恒成立∵f(0)=1∴f(x)≥f(1)f'(x)=e^x-kx-1当k≤0时,f'(x)为增函数∴f'(x)≥f'(0)=e^0-1=0∴f(x)为[0,+∞)上的增函数∴f(x)≥f(0)=1当k>0时,f'(x)=e^x-kx-1f''(x)=e^x-k当01...