Cho hàm số y = f(x) thỏa mãn f'(x)

* Hướng dẫn giải

Đáp án B

Ta có: $f\text{'}\left(x\right).f\left(x\right)=x^4+x^2\Rightarrow \int f\text{'}\left(x\right).f\left(x\right)dx=\int \left(x^4+x^2\right)dx$

   $\iff \int f\left(x\right).d\left(f\left(x\right)\right)=\frac{x^5}{5}+\frac{x^3}{3}+C\iff \frac{f^2\left(x\right)}{2}=\frac{x^5}{5}+\frac{x^3}{3}+C$

mà $f\left(0\right)=2\Rightarrow f^2\left(0\right)=4\Rightarrow C=2\Rightarrow \frac{x^5}{5}+\frac{x^3}{3}+2$

Vậy $f^2\left(2\right)=2\left(\frac{x^5}{5}+\frac{x^3}{3}+2\right)\left|\begin{array}{l}\\ x=2\end{array}\right.=\frac{332}{15}$