csat-suneung 2009 Q29

csat-suneung · South-Korea · csat__math-science 4 marks Chain Rule Derivative of Inverse Functions

(Calculus) Let the function $f(x)$ be defined as $$f(x) = \int_a^x \{2 + \sin(t^2)\} dt$$ If $f''(a) = \sqrt{3}a$, find the value of $(f^{-1})'(0)$. (Given: $a$ is a constant satisfying $0 < a < \sqrt{\frac{\pi}{2}}$) [4 points]
(1) $\frac{1}{10}$
(2) $\frac{1}{5}$
(3) $\frac{3}{10}$
(4) $\frac{2}{5}$
(5) $\frac{1}{2}$

(Calculus) Let the function $f(x)$ be defined as
$$f(x) = \int_a^x \{2 + \sin(t^2)\} dt$$
If $f''(a) = \sqrt{3}a$, find the value of $(f^{-1})'(0)$.\\
(Given: $a$ is a constant satisfying $0 < a < \sqrt{\frac{\pi}{2}}$) [4 points]\\
(1) $\frac{1}{10}$\\
(2) $\frac{1}{5}$\\
(3) $\frac{3}{10}$\\
(4) $\frac{2}{5}$\\
(5) $\frac{1}{2}$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q26 Q26b Q27 Q27b Q28 Q28b Q29 Q29b Q30