Question

Help me answer 1(e), thank you!The derivative of f(x) = 240(1-x/30) is f'(x) = -8x

Answer 1

1.(e) Given:

The derivative of

`f(x)=240(1-(x)/(30))\text{ is }f^(\prime)(x)=-8x`

To find: True or false?

Step-by-step explanation:

We have given the function

`f(x)=240(1-(x)/(30))`

Differentiate f(x) with respect to x

We get

`\begin{gathered} (d)/(dx)[f^(x_)]=(d)/(dx)[240(1-(x)/(30))] \\ \\ f^(\prime)(x)=240.[(d)/(dx)(1)-(d)/(dx)((x)/(30))] \\ \\ f^(\prime)(x)=240.[0-(1)/(30).(d)/(dx)(x)] \\ \\ f^(\prime)(x)=240.[0-(1)/(30)*1].......\lbrace(d)/(dx)(x)=1\rbrace \\ \\ f^(\prime)(x)=240.[-(1)/(30)] \\ \\ f^(\prime)(x)=-(240)/(30) \\ \\ f^(\prime)(x)=-8 \end{gathered}`

Hence,

`f^(\prime)(x)=-8`

Therefore,

The derivative of

`\begin{equation*} f(x)=240(1-(x)/(30))\text{ is }f^(\prime)(x)=-8 \end{equation*}`

Answer: The given statement is False.

The derivative of f(x) = 240(1-x/30) is f'(x) = -8x : False.