Find the derivative at x=2 of the function f( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We have the function $f(x) = 3x$.To find the derivative at $x=2$,we use the definition of the derivative:$f'(2) = \lim_{h 	o 0} \frac{f(2+h) - f(

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) We have the function $f(x) = 3x$.To find the derivative at $x=2$,we use the definition of the derivative:$f'(2) = \lim_{h 	o 0} \frac{f(2+h) - f(2)}{h}$Substituting $f(x) = 3x$ into the formula:$f'(2) = \lim_{h 	o 0} \frac{3(2+h) - 3(2)}{h}$$f'(2) = \lim_{h 	o 0} \frac{6 + 3h - 6}{h}$$f'(2) = \lim_{h 	o 0} \frac{3h}{h}$$f'(2) = \lim_{h 	o 0} 3 = 3$Thus,the derivative of the function $f(x) = 3x$ at $x=2$ is $3$.

Find the derivative at $x=2$ of the function $f(x)=3x$.

Similar Questions

Find the derivative of the function $(ax + b)^n$ with respect to $x$,where $a$ and $b$ are fixed non-zero constants and $n$ is an integer.

Find the derivative of the following function from first principles: $\cos \left(x-\frac{\pi}{8}\right)$

Let $f(x) = 3x^{10} - 7x^{8} + 5x^{6} - 21x^{3} + 3x^{2} - 7$. Then $\lim_{h \rightarrow 0} \frac{f(1-h) - f(1)}{h^{3} + 3h}$ is:

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

Find the derivative of $f(x) = x$ at $x = 1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module