Find k such that the line is tangent to the graph of the function. Function Line f(x) - kx y = Sx + 20 Step 1 We want a value of k that will make the line y tangent to the function f(x). In order for y to be tangent to f(x), then y will touch f(x) at a point. At that point, the two equations are equal. fx) - Y k - 5 20 Step 2 If y is tangent to f(x) at the point x, the slope of y must equal the derivative of x). To determine this we simply take the derivative of each side of the equation. kx- Sx + 20 kV xk 5x + 20] Step 3 To find the derivative of the left side of the equation, rewrite the square root using exponents and use the Power Rule. Use the Sum Rule and the Constant Multiple Rule to solve the right side. -5x + 20) 5x+ 20 dx xp %3D5

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