csat-suneung 2024 Q7

csat-suneung · South-Korea · csat__math 3 marks Stationary points and optimisation Find critical points and classify extrema of a given function

For the function $f(x) = \frac{1}{3}x^3 - 2x^2 - 12x + 4$, if $f$ has a local maximum at $x = \alpha$ and a local minimum at $x = \beta$, find the value of $\beta - \alpha$. (Here, $\alpha$ and $\beta$ are constants.) [3 points]
(1) $-4$
(2) $-1$
(3) 2
(4) 5
(5) 8

For the function $f(x) = \frac{1}{3}x^3 - 2x^2 - 12x + 4$, if $f$ has a local maximum at $x = \alpha$ and a local minimum at $x = \beta$, find the value of $\beta - \alpha$. (Here, $\alpha$ and $\beta$ are constants.) [3 points]\\
(1) $-4$\\
(2) $-1$\\
(3) 2\\
(4) 5\\
(5) 8

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