1
y=x³-48x+17
y`=3x²-48=3(x-4)(x+4)=0
x=4 x=-4
+ _ +
--------------(-4)---------------(4)------------------
max
ymax=y(-4)=-64+192+17=145
2
y=-x/(x²+225)
y`=(-x²-225+2x²)/(x²+225)²=(x²-225)/(x²+225)²=0
x²=225
x=-15 x=15
+ _ +
--------------(-15)---------------(15)------------------
max
ymax(-15)=15/(225+225)=15/450=1/30
3
y=(x-2)²(x-4)+5
y`=2(x-2)(x-4)+(x-2)²*1=(x-2)(2x-8+x-2)=(x-2)(3x-10)=0
x=2 x=3 1/3
+ _ +
--------------(2)---------------(3 1/3)------------------
max
ymax=y(2)=(2-2)²(2-4)+5=5