- y = mx + b is a linear equation and represents a straight line. (The direction m is constant

Carl Hood

Carl Hood

Answered question

2022-03-02

- y=mx+b is a linear equation and represents a straight line. (The direction m is constant.)
- y=x2+b is quadratic and represents a parabola. (The direction of the tangent is not constant.)
- But y=x2=xx in linear form with the first x being the direction and y intercept being 0 in this case.
So you could say that indeed the direction depends upon x.
However, for x=1,m=2 and not 1 and indeed the derivative of x2 is 2x.
Why? Where does the 2 come from?

Answer & Explanation

Alissia Head

Alissia Head

Beginner2022-03-03Added 5 answers

Since both the terms in the product xx are changing with x, you must use the product rule:
xx
For a small change in x's:
(x+Δx)(x+Δx)
Take the difference
(x+Δx)(x+Δx)xx
Simplifying gives
xΔx+Δxx+ΔxΔx
Divide by Δx
x+x+Δx
Since Δx goes to 0 as the secant approaches the tangent... see where the 2x comes from?

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