1.(e) Given:
The derivative of
[tex]f(x)=240(1-\frac{x}{30})\text{ is }f^{\prime}(x)=-8x[/tex]
To find: True or false?
Explanation:
We have given the function
[tex]f(x)=240(1-\frac{x}{30})[/tex]
Differentiate f(x) with respect to x
We get
[tex]\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}[/tex]
Hence,
[tex]f^{\prime}(x)=-8[/tex]
Therefore,
The derivative of
[tex]\begin{equation*} f(x)=240(1-\frac{x}{30})\text{ is }f^{\prime}(x)=-8 \end{equation*}[/tex]
Answer: The given statement is False.
The derivative of f(x) = 240(1-x/30) is f'(x) = -8x : False.
