A curve has the equation $$$y=x^{3}+8 x^{2}+5 x$$$. Work out the coordinates of the two turning points. $$\[ (..................., ...................) \text { and }(...................,...................) \]$$

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_s20_qp_41 Year：2020 Question No：10(b)(i)

Answer:

$\left(-\frac{1}{3},-\frac{22}{27}\right)$ oe and $(-5,50)$

Knowledge points:

E2.13.1 Understand the idea of a derived function.

E2.13.2

E2.13.3 Apply differentiation to gradients and turning points (stationary points).

E2.13.4 Discriminate between maxima and minima by any method.

E2.5.1 Derive and solve linear equations in one unknown

E2.5.2 Derive and solve simultaneous linear equations in two unknowns.

E2.5.3 Derive and solve simultaneous equations, involving one linear and one quadratic.

E2.5.4 Derive and solve quadratic equations by factorisation, completing the square and by use of the formula.

E2.5.5 Derive and solve linear inequalities. (Including representing and interpreting inequalities on a number line.) (Interpretation of results may be required.)

A curve has the equation $$\(y=x^{3}+8 x^{2}+5 x\)$$. Work out the coordinates of the two turning points. $$\[ (..................., ...................) \text { and }(...................,...................) \]$$

Answer:

Knowledge points:

Solution:

A curve has the equation $$\(y=x^{3}+8 x^{2}+5 x\)$$. Work out the coordinates of the two turning points. $$\[ (..................., ...................) \text { and }(...................,...................) \]$$

Answer:

Knowledge points:

Solution:

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