Find the x and y coordinates of the minimum of the following equation: y = x^2 - 14x + 55.
We can see that the quadratic function will be U-shaped, as the quadratic term is with a positive sign. Therefore, the absolute extreme of the function will be a minimum. Step 1: Differentiate to find the slope of the function. dy/dx = 2x - 14Step 2: Find where the slope equals 0. This will be the x coordinate. 2x -14 = 0 2x = 14 x = 7Step 3: Substitute x into the original equation, to get the functions value at x. y = 7^2 - (14 x 7) +55 y = 49 - 98 + 55 y = 104 - 98 y = 6Step 4: We have our coordinates: (7,6)
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