Find the derivative of x^{2}-2 at x=10. | vedclass

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(C) Let $f(x) = x^{2} - 2$.To find the derivative at $x = 10$,we use the definition of the derivative:$f'(10) = \lim_{h 	o 0} \frac{f(10+h) - f(10)}{

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Let $f(x) = x^{2} - 2$.To find the derivative at $x = 10$,we use the definition of the derivative:$f'(10) = \lim_{h 	o 0} \frac{f(10+h) - f(10)}{h}$Substitute $f(x) = x^{2} - 2$ into the formula:$f'(10) = \lim_{h 	o 0} \frac{[(10+h)^{2} - 2] - [10^{2} - 2]}{h}$Expand the terms:$f'(10) = \lim_{h 	o 0} \frac{100 + 20h + h^{2} - 2 - 100 + 2}{h}$Simplify the expression:$f'(10) = \lim_{h 	o 0} \frac{20h + h^{2}}{h}$Divide by $h$:$f'(10) = \lim_{h 	o 0} (20 + h)$Evaluate the limit as $h 	o 0$:$f'(10) = 20 + 0 = 20$Thus,the derivative of $x^{2} - 2$ at $x = 10$ is $20$.

Find the derivative of $x^{2}-2$ at $x=10$.

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