New Zealand
Level 7 - NCEA Level 2

# Families of Anti-Derivatives and Specific Anti-Derivatives

## Interactive practice questions

Consider the gradient function $f'\left(x\right)$f(x)$=$=$2$2.

a

The family of the antiderivative, $f\left(x\right)$f(x), will be:

Exponential

A

Cubic

B

Linear

C

D

Exponential

A

Cubic

B

Linear

C

D
b

The form of the antiderivative will be $f\left(x\right)$f(x)$=$=$mx+c$mx+c. State the value of $m$m.

c

Which of the following functions represent possible values for an antiderivative $f\left(x\right)$f(x)?

Select all that apply.

$f\left(x\right)=-2x$f(x)=2x

A

$f\left(x\right)=2x+6$f(x)=2x+6

B

$f\left(x\right)=2x-3$f(x)=2x3

C

$f\left(x\right)=-2x+6$f(x)=2x+6

D

$f\left(x\right)=-2x$f(x)=2x

A

$f\left(x\right)=2x+6$f(x)=2x+6

B

$f\left(x\right)=2x-3$f(x)=2x3

C

$f\left(x\right)=-2x+6$f(x)=2x+6

D
Easy
Approx a minute

Consider the gradient function $f'\left(x\right)$f(x)$=$=$6$6.

Consider the gradient function $f'\left(x\right)$f(x)$=$=$-8x$8x.

Consider the gradient function $f'\left(x\right)$f(x)$=$=$4x+3$4x+3.

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems