Given a point (1,7) on the image of function y = 2x ^ 2 + 5 and its adjacent point (1 + △ x, 7 + △ y), then △ Y / △ x=

Given a point (1,7) on the image of function y = 2x ^ 2 + 5 and its adjacent point (1 + △ x, 7 + △ y), then △ Y / △ x=

Y '= 4x, when x = 1, y' = 4
When its adjacent point is infinitely close to (1,7), the slope between the two points is exactly the tangent slope of (1,7)
So △ Y / △ x = (7 + △ Y-7) / (1 + △ x-1) = y '= 4