Step 1

The derivative properties:

\(\frac{d}{dx}(f(x)\ -\ a)=f'(x)\)

\(\frac{d}{dx}(af(x))=af'(x)\)

calculate the derivative of \(g(x) = f(x)\ -\ 2\) with respect to x as follows

\(g'(x)=\frac{d}{dx}(f(x)\ -\ 2)\)

\(= f'(x)\)

Step 2

Now calculate the derivative of \(h(x) = 2f(x)\) with respect to x as follows

\(h'(x)=\frac{d}{dx}=(2f(x))\)

\(= 2f'(x)\)

\(\therefore h'(x) = 2 f'(x)\)

Step 3

Now calculate the derivative of \(r(x) = f(-3x)\) with respect to x as follows

\(r'(x)=\frac{d}{dx}=f(-3x)\)

\(=\ - 3f'(-3x)\)

As \(r'(x) =\ -3f'(-3x),\) compute the the value of

\(-3f'(-3x)\)

\(r'(-2) = 3f' [-3\ (2)]\)

\(= -3 f'(6)\)

Here \(r'(-2) =\ -3f'(6)\) cannot be computed the values

of \(f'(6)\) is not known.

\(r'(-1) =\ -3f' [-3\ (-1)]\)

\(=\ -3f' (3)\)

\(=\ -3 (-5)\)

\(= 15\)

\(r'(0) =\ -3f'[-3\ (0)]\)

\(= -3(-\frac{1}{3})\)

\(= 1\)

And \(r'(1) =\ -3f[-3\ (1)]\)

\(=\ -3 f' (-3)\)

Hense \(-3 f'(-3)\) can not be compluted.

The derivative properties:

\(\frac{d}{dx}(f(x)\ -\ a)=f'(x)\)

\(\frac{d}{dx}(af(x))=af'(x)\)

calculate the derivative of \(g(x) = f(x)\ -\ 2\) with respect to x as follows

\(g'(x)=\frac{d}{dx}(f(x)\ -\ 2)\)

\(= f'(x)\)

Step 2

Now calculate the derivative of \(h(x) = 2f(x)\) with respect to x as follows

\(h'(x)=\frac{d}{dx}=(2f(x))\)

\(= 2f'(x)\)

\(\therefore h'(x) = 2 f'(x)\)

Step 3

Now calculate the derivative of \(r(x) = f(-3x)\) with respect to x as follows

\(r'(x)=\frac{d}{dx}=f(-3x)\)

\(=\ - 3f'(-3x)\)

As \(r'(x) =\ -3f'(-3x),\) compute the the value of

\(-3f'(-3x)\)

\(r'(-2) = 3f' [-3\ (2)]\)

\(= -3 f'(6)\)

Here \(r'(-2) =\ -3f'(6)\) cannot be computed the values

of \(f'(6)\) is not known.

\(r'(-1) =\ -3f' [-3\ (-1)]\)

\(=\ -3f' (3)\)

\(=\ -3 (-5)\)

\(= 15\)

\(r'(0) =\ -3f'[-3\ (0)]\)

\(= -3(-\frac{1}{3})\)

\(= 1\)

And \(r'(1) =\ -3f[-3\ (1)]\)

\(=\ -3 f' (-3)\)

Hense \(-3 f'(-3)\) can not be compluted.