Zadanie 8a
Show that a=1 and b=−6.
Second derivatives and linked graphs
Interpret higher-gradient information and relate the graphs and signs of a function and its first two derivatives.
Tę umiejętność sprawdza 13 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 13 Otwórz w wyszukiwarce z filtrami
Zadanie 9c
(i) Show that . (ii) Find the inflection point P.
Zadanie 9d
Given h′′(x) = e3x(9x2 − 6x + 2)/x3, prove that the curve has no inflection point.
Zadanie 3b
Find the interval on which its graph is concave up.
Zadanie 8c
Find c.
Zadanie 7a
Find (i) y′; (ii) y″.
Zadanie 8b
(i) State where f′(x) = 0. (ii) Show that f′′(x) = (−8x2 + 32x − 20)/(2x2 − 8x + 11)2. (iii) Hence justify that the stationary point is a local minimum.
Zadanie 7d
(i) Show that h′′(x) = 3(x + 3)ex. (ii) Find where the graph is concave up.
Zadanie 7c
For S(x) = 108/x + 3πx2 and a = (18/π)1/3: (i) find S″(x); (ii) use S″ to justify a minimum at a; (iii) find the minimum area.
Zadanie 7c
For S(x) = 108/x + 3πx2 and a = (18/π)1/3: (i) find S″(x); (ii) use S″ to justify a minimum at a; (iii) find the minimum area.
Zadanie 7d
Sketch f″, labelling its x- and y-intercepts.
Zadanie 7e
(i) State the x-coordinate of the inflection point of f. (ii) Find where f is concave down, justifying your answer.
Zadanie 7e
Find where y=g(x) is concave up.