Mcguire Ford
01/26/2024 · Middle School
Determina la estimación de la derivada de la función \( f(x) = 4x^3 - x + 6\) en el punto \( x = 0\).
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Find the first order derivative with respect to \( x \) for \( 4x^3 - x + 6 \).
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
\(\frac{d}{dx}\left(4x^{3}-x+6\right)\)
- step1: Use differentiation rules:
\(\frac{d}{dx}\left(4x^{3}\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(6\right)\)
- step2: Calculate:
\(12x^{2}-1+0\)
- step3: Remove 0:
\(12x^{2}-1\)
Substitute \( x=0 \) into the expression \( 12x^2 - 1 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(12x^{2}-1\)
- step1: Substitute:
\(12\times 0^{2}-1\)
- step2: Calculate:
\(12\times 0-1\)
- step3: Multiply:
\(0-1\)
- step4: Remove 0:
\(-1\)
La derivada de la función \( f(x) = 4x^3 - x + 6 \) es \( 12x^2 - 1 \). Al evaluarla en el punto \( x = 0 \), obtenemos que la estimación de la derivada en ese punto es -1.
Quick Answer
La derivada de \( f(x) = 4x^3 - x + 6 \) en \( x = 0 \) es -1.
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