The equation of a curve is $$\(y=54 x-(2 x-7)^{3}\)$$. Determine the nature of each of the stationary points. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：10(c)
Answer:
\(x=5 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-72 \rightarrow\) Maximum
(FT only for omission of ' \(\times 2\) ' from the bracket)
\(x=2 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=72 \rightarrow\) Minimum
(FT only for omission of ' \(\times 2\) ' from the bracket)
(FT only for omission of ' \(\times 2\) ' from the bracket)
\(x=2 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=72 \rightarrow\) Minimum
(FT only for omission of ' \(\times 2\) ' from the bracket)
Knowledge points:
1.7.4 locate stationary points and determine their nature, and use information about stationary points in sketching graphs. (Including use of the second derivative for identifying maxima and minima; alternatives may be used in questions where no method is specified.) (Knowledge of points of inflexion is not included.)
Solution:
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