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Numerade Educator

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Problem 21 Easy Difficulty

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.

$ f(x) = 3x - 8 $

Answer

$\lim _{h \rightarrow 0} \frac{3 h}{h}=\lim _{h \rightarrow 0} 3=3$

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Video Transcript

in this problem, we have F of X equals three x minus eight. The domain uh For dysfunction uh consists of all values of X for which dysfunction would be defined. Uh The domain basically is going to be all real numbers X can be any real number because dysfunction three times x minus eight will be defined for any real number. So the domain is to set up all real numbers where you can think of it as the entire X axis. Now the derivative of F with respect to X. F. Prime of X. If we differentiate our function F of X equals three X minus eight with respect to X, the derivative of three X is three. Ah the derivative of a constant is zero. So the derivative with respect to X F prime of X is three. The domain of this derivative function. Well, since it's equal to the constant three, regardless of what X is once again, X could be any real numbers. So the domain is the set of all real numbers or the entire X. Axis.