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Let F(X)=(X−8)(6x+7). Find An Equation For The Tangent Line To The Graph Of F At X=6. Tangent Line: Y= ___________

User Eang
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Final answer:

To find the equation of the tangent line to the graph of F(X) = (X-8)(6X+7) at X = 6, we take the derivative of the function to find the slope, then use the point-slope form of a linear equation.

Step-by-step explanation:

To find the equation of the tangent line to the graph of F(X) = (X-8)(6X+7) at X = 6, we need to find the slope of the tangent line at that point and use the point-slope form of a linear equation.

To find the slope, we take the derivative of the function F(X) and evaluate it at X = 6. The derivative of F(X) = (X-8)(6X+7) is 6(6X+7) + (X-8)(6), which simplifies to 42X + 42. When evaluated at X = 6, we get a slope of 270.

Now we can use the point-slope form, which is Y - y = m(X - x), where (x, y) is the given point and m is the slope. Plugging in X = 6 and Y = F(6) into the equation, we get Y - F(6) = 270(X - 6). Simplifying further gives us Y - F(6) = 270X - 1620. This is the equation of the tangent line.

User Empi
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