NZ Level 8 (NZC) Level 3 (NCEA) [In development] Identifying turning points and points of inflection

## Interactive practice questions

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

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?

A

B

C

D

A

B

C

D
Easy
Approx 4 minutes

Consider the function $y=-\left(x-1\right)^2\left(x+2\right)$y=(x1)2(x+2) graphed below.

Consider the function $y=\left(x-11\right)\left(x+13\right)\left(x+4\right)$y=(x11)(x+13)(x+4) graphed below.

Consider the function $y=-\left(x+13\right)\left(x-2\right)\left(x-11\right)$y=(x+13)(x2)(x11) graphed below.

### Outcomes

#### M8-11

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

#### 91578

Apply differentiation methods in solving problems