Consider the function $f^{\prime \prime}(x)=\sec ^4 x+4$ with $f(0)=0$ and $f^{\prime}(0)=0$. What is $f(x)$ equal to?

• Correct answer
  A

  $\frac{2 \ln \sec x}{3}+\frac{\tan ^2 x}{6}+2 x^2$
• B

  $\frac{3 \ln \sec x}{2}+\frac{\cot ^2 x}{6}+2 x^2$
• C

  $\frac{4 \ln \sec x}{3}+\frac{\sec ^2 x}{6}+2 x^2$
• D

  $\ln \sec x+\frac{\tan ^4 x}{12}+2 x^2$

Hence, the correct answer is option: 'A'.