1. y'=u'v+v'u u=√x u'=1/2√x v =(15-3x) v'=-3
y'=1/(2√x)*(15-3x)-3√x
2. y'=(u/v)'=1/v²[u'v-v'u] u=8x-12 u'=8 v=x+14 v'=1
y'=1/(x+14)²[8(x+14)+1*(8x-12)]
3. y'=-2sin(9x+π/2)*9=-18sin(9x+π/2)
4. y'=3(25x-15)²*25=75(25x-15)²
5. y=5log₃(4x-1) y'=5/[4(4x-1)ln3]
6. y=3x⁴-16x³+24x²-11 y'=12x³-48x²+24=0
x³-4x²+2=0 точки экстремума
D=16-8=8 √8=2√2
x1=0.5[4+2√2] x2=0.5[4-2√2]
7. y=4x⁴+4x³+1 [-2;1]
x=-2 y=64-32+1=33 x=1 y=4+4+1=9
y'=16x³+12x²=4x²(4x+3)=0
x=0 y=1 x=-3/4=-0.75 y=1,265625-1,6875+1=0,578125
ymin=0,578125 ymax=33
8. y=x^3+x^2-x-1 y'=3x²+2x-1=0 x1=-1 3x²+2x-1/x+1=3x-1 x2=1/3
----------------- -1------------------1/3-------------------
+↑ -↓ + ↑
x=-1 max x=1/3 min
