Quick questions on Implicit differentiation and second derivatives: VCE Specialist Mathematics Unit 3

Q: What is not using the product rule for xy?

(d)/(dx)[xy] = y + x(dy)/(dx). Both terms are needed.

Q: What is q2?

State the concavity of y = e^x everywhere. [1 mark]

Q: What is q3?

Find any points of inflection of y = x^3 - 3x. [3 marks]

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is not using the product rule for

xy

Show answer

\frac{d}{dx}[xy] = y + x\frac{dy}{dx}

. Both terms are needed.

What is q1?

Show answer

Find

\frac{dy}{dx}

for

x^2 - y^2 = 9

by implicit differentiation. [2 marks]

What is q2?

Show answer

State the concavity of

y = e^x

everywhere. [1 mark]

What is q3?

Show answer

Find any points of inflection of

y = x^3 - 3x

. [3 marks]

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