How do you find the slope of the graph f(x)=(2x+1)^2 at (0,1)?

1 Answer

Using the chain rule of derivatives, and then plugging in a x value of 0 for the f'(x) function, you get a slope.

Explanation:

Consider
F(x)=fprime(g(x))*gprime(x) This what we define as the chain rule, "first the outside derivative then the inside derivative"
If f(x)=(2x+1)^2
and f'(x)=8x+4
and when f'(0)=8(0)+4=4
Then the slope equals 4.

Proof Thing:
Derivatives are slopes of functions.
We know this by the formal definition of f'(x)=(f(x+h)-f(x))/h
and m=(y_2-y_1)/(x_2-x_1)
They are similar because that is how the definition came by substituting them as (Deltay)/(Deltax); where h represents the change the function.
So, derivatives find a slope of a function.
We simplify the process by using various derivative rules