Find the derivative of 99x at x=100. | vedclass

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Question

(A) Let $f(x) = 99x$.By the definition of the derivative,$f'(a) = \mathop{\lim}\limits_{h 	o 0} \frac{f(a+h) - f(a)}{h}$.Here,$a = 100$,so $f'(100) =

Vedclass · Accepted Answer

$99$

Vedclass · Answer

(A) Let $f(x) = 99x$.By the definition of the derivative,$f'(a) = \mathop{\lim}\limits_{h 	o 0} \frac{f(a+h) - f(a)}{h}$.Here,$a = 100$,so $f'(100) = \mathop{\lim}\limits_{h 	o 0} \frac{f(100+h) - f(100)}{h}$.Substituting $f(x) = 99x$:$f'(100) = \mathop{\lim}\limits_{h 	o 0} \frac{99(100+h) - 99(100)}{h}$.$f'(100) = \mathop{\lim}\limits_{h 	o 0} \frac{9900 + 99h - 9900}{h}$.$f'(100) = \mathop{\lim}\limits_{h 	o 0} \frac{99h}{h}$.$f'(100) = \mathop{\lim}\limits_{h 	o 0} (99) = 99$.Thus,the derivative of $99x$ at $x=100$ is $99$.

Find the derivative of $99x$ at $x=100$.

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