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