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Find the slope of the tangent line to the graph of 7y3−y2−11=x7y^3 - y^2 - 11 = x at (−5,1)(-5,1).

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Full solution

Q. Find the slope of the tangent line to the graph of 7y3−y2−11=x7y^3 - y^2 - 11 = x at (−5,1)(-5,1).
  1. Find Derivative with Implicit Differentiation: First, we need to find the derivative of the equation with respect to xx to get the slope formula. Since the equation is implicitly defined, we use implicit differentiation.
  2. Solve for dydx\frac{dy}{dx}: Now, solve for dydx\frac{dy}{dx} to find the slope of the tangent line.
  3. Substitute y=1y = 1: Substitute y=1y = 1 into the derivative to find the numerical value of the slope at the point (−5,1(-5,1).

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