已知f(x)=ax^2+bx+c,且f(1)=2,f`(0)=0,∫ ( 上1下-1) f(x)dx=-4,求a,b,c
1个回答

f(x) = ax² + bx + c

f(1) = 2 → a + b + c = 2

f'(x) = 2ax + b

f'(0) = 2a(0) + b = 0 → b = 0

∫(-1→1) f(x) dx = ∫(-1→1) (ax² + c) dx = - 4

ax³/3 + cx |(-1→1) = - 4

(a/3 + c) - (- a/3 - c) = - 4

{ 2a/3 + 2c = - 4

{ a + c = 2,将b = 0代入第二步得出

解方程得a = 6,c = - 4

∴a = 6,b = 0,c = - 4

相关问题