Solved: "How do you find the slope of the..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Emmy Decker

Answered question

2022-04-11

How do you find the slope of the graph

f (x) = {(2 x + 1)}^{2}

at (0,1)?

Answer & Explanation

cutimnm135imsa

Beginner2022-04-12Added 21 answers

Consider
F(x)=f'(g(x))*g'(x) This what we define as the chain rule, "first the outside derivative then the inside derivative"
If

f (x) = {(2 x + 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) = \frac{f (x + h) - f (x)}{h}

and

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

They are similar because that is how the definition came by substituting them as

\frac{△ y}{△ x}

; where h represents the change the function.
So, derivatives find a slope of a function.
We simplify the process by using various derivative rules

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