If f(x)=x^2-4x, find f(x+trianglex)
The triangle in the test paper is a symbol I just don't know how to put symbol here.
The answer is (x+trianglex)(x+trianglex-4), the problem is I don't know how it became like that.
when you write f(x) = x^2-4x, the "x" is just the name of the argument. You can replace it with whatever you want. So,
f(2) = 2^2 - 4*2
So,
f(x) = x(x-4)
f(x+∆x) = (x+∆x)(x+∆x - 4)
Surely by this time you have learned that ∆ is the Greek letter "delta" and is used to indicate a small change in the variable x.
Oobleck can u come help me
yeah - I'll be right over...
To find f(x + Δx), we need to substitute (x + Δx) into the equation for f(x).
Given f(x) = x^2 - 4x, we can substitute (x + Δx) into the equation:
f(x + Δx) = (x + Δx)^2 - 4(x + Δx)
Now let's expand and simplify this expression:
Step 1: Expand (x + Δx)^2 using the square of a binomial formula.
(x + Δx)^2 = x^2 + 2xΔx + (Δx)^2
Step 2: Substitute the expanded expression back into f(x + Δx).
f(x + Δx) = x^2 + 2xΔx + (Δx)^2 - 4(x + Δx)
Step 3: Distribute -4 into (x + Δx).
f(x + Δx) = x^2 + 2xΔx + (Δx)^2 - 4x - 4Δx
Step 4: Combine like terms.
f(x + Δx) = x^2 - 4x + 2xΔx - 4Δx + (Δx)^2
Step 5: Rearrange the terms to group like terms.
f(x + Δx) = x^2 - 4x + (2xΔx - 4Δx) + (Δx)^2
Step 6: Factor out Δx from the second and third terms.
f(x + Δx) = x^2 - 4x + 2Δx(x - 2) + (Δx)^2
So the expression for f(x + Δx) is (x^2 - 4x + 2Δx(x - 2) + (Δx)^2).
Notice that the last term is (Δx)^2; this is the triangle-like symbol you mentioned. In mathematics, Δx is often used to represent a change in x or a small increment in x. The Δ (pronounced "delta") is the Greek letter "delta," which is commonly used as a symbol for "change" in mathematics. Therefore, when Δx is squared, it is written as (Δx)^2.
Therefore, the final expression for f(x + Δx) is (x^2 - 4x + 2Δx(x - 2) + (Δx)^2).