Grade 12 Maths · Calculus

Find concavity and inflection point

Use the second derivative to find the point of inflection and where a curve bends upward or downward (for example f″(x) > 0 means concave up).

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Inflection Point Grade 12Kevinmathscience

Concavity Grade 12: Where is graph concave down?Kevinmathscience

Concavity, Inflection Points, and Second DerivativeThe Organic Chemistry Tutor

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Question 9.3 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

Given:

f (x) = x^{3} - 6 x^{2} + 9 x - 4 = (x - 4) (x - k)^{2}

9.3 Describe the concavity of

f

x = - 3

.(2)

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