Differentiation

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Identifying turning points and points of inflection

Consider the function $y=\left(x+4\right)^2\left(x+1\right)$`y`=(`x`+4)2(`x`+1) graphed below.

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a

State the $x$`x`-coordinate(s) of the turning point(s) of the function.

If there is more than one turning point, write all the values on the same line, separated by commas.

b

What is the gradient at these turning points?

c

State the $x$`x`-coordinate of the point of inflection.

d

Which of the following is correct?

The gradient is positive at the point of inflection.

A

The gradient is negative at the point of inflection.

B

The gradient is positive at the point of inflection.

A

The gradient is negative at the point of inflection.

B

e

Which of the following could be the graph of the gradient function?

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A

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B

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C

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D

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A

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B

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C

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D

Easy

Approx 4 minutes

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Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

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