Find the Coordinates of the point on the curve y=4x+x^-1 where the gradient is zero?

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y = 4x + 1/x
dy/dx = 4 - 1/x^2 = 0
1/x^2 = 4
x^2 = 1/4
x = ± 1/2

y(1/2) = 4(1/2) + 2 = 4
y(-1/2) = 4(-1/2) - 2 = -4

The points are (1/2, 4) and (-1/2, -4)....Show more

f'(x) = -6x + 2. f'(a million) = -6(a million) + 2 = -4. So it fairly is m = slope of the tangent line. f(a million) = -3 + 2 - a million = -2. So your (x, y) ingredient is at (a million, -2). Plug into y = mx + b. -2 = (-4)(a million) + b. -2 = -4 + b. b = 6. Equation: y = -4x + 6....Show more

Simple differentiate and set that equation to 0 and solve for x and y...Show more