csat-suneung 2024 Q27_calculus

csat-suneung · South-Korea · csat__math 3 marks Differentiating Transcendental Functions Evaluate derivative at a point or find tangent slope
For a real number $t$, let $f(t)$ denote the slope of the line passing through the origin and tangent to the curve $y = \frac{1}{e^x} + e^t$. For the constant $a$ satisfying $f(a) = -e\sqrt{e}$, find the value of $f'(a)$. [3 points]
(1) $-\frac{1}{3}e\sqrt{e}$
(2) $-\frac{1}{2}e\sqrt{e}$
(3) $-\frac{2}{3}e\sqrt{e}$
(4) $-\frac{5}{6}e\sqrt{e}$
(5) $-e\sqrt{e}$ 
For a real number $t$, let $f(t)$ denote the slope of the line passing through the origin and tangent to the curve $y = \frac{1}{e^x} + e^t$. For the constant $a$ satisfying $f(a) = -e\sqrt{e}$, find the value of $f'(a)$. [3 points]\\
(1) $-\frac{1}{3}e\sqrt{e}$\\
(2) $-\frac{1}{2}e\sqrt{e}$\\
(3) $-\frac{2}{3}e\sqrt{e}$\\
(4) $-\frac{5}{6}e\sqrt{e}$\\
(5) $-e\sqrt{e}$
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 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry