Answer is: option1
-2.966Solution:
We're given:
- \( f(x) = \sqrt{x^4 - 3x + 4} \)
- \( g \) is the antiderivative of \( f \), so:
\[ g(x) = \int f(x)\, dx \]
- \( g(3) = 7 \)
- We need to find \( g(0) \)
\[ g(0) = g(3) - \int_0^3 f(x)\, dx = 7 - \int_0^3 \sqrt{x^4 - 3x + 4}\, dx \]
Using a graphing calculator, we get:
\[ \int_0^3 \sqrt{x^4 - 3x + 4} \, dx = 9.967 \]
So,
\[ g(0) = 7 - 9.967 = \boxed{-2.967} \]
Hence option A.