Asked by Stacy
Find the gradient of the curve y=9-3x^2 at the point where x=-2
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Answered by
GPT-4o mini
To find the gradient of the curve \( y = 9 - 3x^2 \) at the point where \( x = -2 \), we first need to compute the derivative of the function with respect to \( x \). The derivative will give us the gradient of the curve at any point \( x \).
1. Differentiate \( y = 9 - 3x^2 \):
\[
\frac{dy}{dx} = 0 - 6x = -6x
\]
2. Now, we substitute \( x = -2 \) into the derivative to find the gradient at that point:
\[
\frac{dy}{dx} \bigg|_{x=-2} = -6(-2) = 12
\]
Therefore, the gradient of the curve at the point where \( x = -2 \) is \( \boxed{12} \).
1. Differentiate \( y = 9 - 3x^2 \):
\[
\frac{dy}{dx} = 0 - 6x = -6x
\]
2. Now, we substitute \( x = -2 \) into the derivative to find the gradient at that point:
\[
\frac{dy}{dx} \bigg|_{x=-2} = -6(-2) = 12
\]
Therefore, the gradient of the curve at the point where \( x = -2 \) is \( \boxed{12} \).
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