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

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

To find: True or false?

Explanation:

We have given the function

$f(x)=240(1-\frac{x}{30})$

Differentiate f(x) with respect to x

We get

$\begin{gathered} \frac{d}{dx}[f^(x_)]=\frac{d}{dx}[240(1-\frac{x}{30})] \\ \\ f^{\prime}(x)=240.[\frac{d}{dx}(1)-\frac{d}{dx}(\frac{x}{30})] \\ \\ f^{\prime}(x)=240.[0-\frac{1}{30}.\frac{d}{dx}(x)] \\ \\ f^{\prime}(x)=240.[0-\frac{1}{30}\times1].......\lbrace\frac{d}{dx}(x)=1\rbrace \\ \\ f^{\prime}(x)=240.[-\frac{1}{30}] \\ \\ f^{\prime}(x)=-\frac{240}{30} \\ \\ f^{\prime}(x)=-8 \end{gathered}$

Hence,

$f^{\prime}(x)=-8$

Therefore,

The derivative of

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

Answer: The given statement is False.

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