Question

Use the alternate definition of derivative to find the derivative.Question: f(x)=3x^2+x

Answer 1

$f^{\prime}(a)=\lim _{x\to a}\frac{f(x)-f(a)}{x-a}$

Procedure:

0. Reeplacing the function

$f^{\prime}(a)=\lim _{x\to a}\frac{(3x^2+x)-(3a^2+a)}{x-a}$$f^{\prime}(a)=\lim _{x\to a}\frac{x(3x+1)-a(3a^{}+1)}{x-a}$$f^{\prime}(a)=\lim _{x\to a}\frac{-(x-a)(-3x-3a-1)}{x-a}$$f^{\prime}(a)=\lim _{x\to a}(3x+3a+1)$$f^{\prime}(a)=3a+3a+1$

Answer:

$f^{\prime}(a)=6a+1$