Question

For the following exercises, the given limit represents the derivative of a function y=f(x) at x=a. Find f(x) and a. limit as h approaches zero: ([3(2+h)^2 +2] - 14)/h

Answer 1

Answer:

$f(x)=3x^2+2$ and the limit is 12

Step-by-step explanation:

we know that the derivative of the function f in x=a is the limit of this

$\dfrac{f(a+h)-f(a)}{a+h-a}=\dfrac{f(a+h)-f(a)}{h}$

as the expression is

$[3(a+h)^2+2 ]-14$

we can say that

     $f(a+h)=3(2+h)^2+2 \\\\f(a)=14$

from the first equation we can identify a = 2 and then

$f(x)=3x^2+2$

to verify that we are correct, we can compute f(2)=3*4+2=14

f'(x)=6x

so f'(2)=12

we can estimate it from the fraction as well

so the limit is 12