Integration

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

Quadratic

D

Exponential

A

Cubic

B

Linear

C

Quadratic

D

b

The form of the antiderivative will be $f\left(x\right)$`f`(`x`)$=$=$mx+c$`m``x`+`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`)=−2`x`

A

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

B

$f\left(x\right)=2x-3$`f`(`x`)=2`x`−3

C

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

D

$f\left(x\right)=-2x$`f`(`x`)=−2`x`

A

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

B

$f\left(x\right)=2x-3$`f`(`x`)=2`x`−3

C

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

D

Easy

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