Question

If f(x) is differential function satisfying 6. ${\int }_0^{1}f\left(t\right)dt=2x^3-3x^2+6x+5,$ then

• A. f(x) is symmetric about x = 1/2
• B. f(x)=0 has no real roots
  
• C. f(x) = 1/2 has two real roots
  
• D. f(x) has minimum at x = 1/2

Answer 1

Answer: (A), (B), (D)

The correct options are
A

f(x) is symmetric about x = 1/2

B

f(x)=0 has no real roots

D

f(x) has minimum at x = 1/2

$6{\int }_0^{x}f\left(t\right)dt=2x^3-3x^2+6x+5\Rightarrow f\left(x\right)=x^2-x+1$