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Find the slope of the tangent line to the graph of −y3+9y2−99=x-y^3 + 9y^2 - 99 = x at (1,5)(1,5).

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Full solution

Q. Find the slope of the tangent line to the graph of −y3+9y2−99=x-y^3 + 9y^2 - 99 = x at (1,5)(1,5).
  1. Find Derivative: First, we need to find the derivative of the given equation to get the slope formula. The equation is −y3+9y2−99=x-y^3 + 9y^2 - 99 = x. We differentiate both sides with respect to yy, treating xx as a constant.
  2. Substitute y=5y=5: Next, substitute y=5y = 5 into the derivative to find the slope at the point (1,5)(1,5).

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