Question

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

Answer 1

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