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Find the slope of the tangent line to the graph of x=−6y2+9y−4x = -6y^2 + 9y - 4 at (−1,1)(-1,1).

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Full solution

Q. Find the slope of the tangent line to the graph of x=−6y2+9y−4x = -6y^2 + 9y - 4 at (−1,1)(-1,1).
  1. Find Derivative: First, we need to find the derivative of the function x=−6y2+9y−4x = -6y^2 + 9y - 4 to find the slope of the tangent line at the point (−1,1)(-1,1). We'll use implicit differentiation, where we differentiate both sides of the equation with respect to yy.
  2. Substitute Value: Next, we substitute y=1y = 1 into the derivative to find the slope of the tangent line at that specific point.
  3. Calculate Slope: Since the slope of the tangent line is the derivative evaluated at the point, the slope at (−1,1)(-1,1) is −3-3.

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