Question

velvety

求解🙏🙏

4. 若實係數三次函數f(x)在x=-3有極小值-24,在x=1有極大值8,則
f(x) =
fix) ax + bx + cx+d
°
+"(x) = bax+b
t'(x)-
30-b
a(x+3)(x-1)
DV
ax+2x-39
+(x)=zax+za

Answer 1

qn

f'(x) = a(x+3)(x-1) = ax²+2ax-3a
f(x) = (a/3)x³+ax²-3ax+b

{ f(-3) = (a/3)(-27)+a(9)-3a(-3)+b = -24
{ f(1) = (a/3)+a-3a+b = 8
↓
{ 9a+b=-24
{ 5a-3b=-24
↓
{ a=-3
{ b=3
→ f(x) = -x³-3x²+9x+3