1)
f(x)=x²*(6-x) [-1;5]
f(x)`=(x²*(6-x))`=0
(x²)`*(6-x)+x²*(6-x)`=2x*(6-x)+x²*(-1)=12x-2x²-x²=12x-3x²=0
3x²-12x=0 |÷3
x²-4x=0
x(x-4)=0
x₁=0 x₂=4
f(-1)=(-1)²*(6-(-1)=1*7=7
f(0)=0²*(6-0)=0=fmin
f(4)=4²*(6-4)=16*2=32=fmax
f(5)=5²*(6-5)=25*1=25.
2)
f(x)=x-sin(2x) [0;π/2]
f(x)`=(x-sin(2x))`=0
1-2*cos(2x)=0
2*cos(2x)=1
cos(2x)=1/2
2x=π/3 x₁=π/6
2x=-π/3 x₂=π/6
f(-π/6)=-π/6-sin(-2*π/6)=-π/6+sin(π/3)=-π/6+π/3=π/6
f(0)=0-sin(2*0)=0
f(π/6)=π/6-sin(2*π/6)=π/6-sin(π/3)=π/6-π/3=-π/6=fmin
f(π/2)=π/2-sin(2*π/2)=π/2-sinπ=π/2-0=π/2=fmax.