Find the coordinates of the stationary point on the curve y=2x^2+3x+4=0
The stationary point on the curve is the point on the curve where the gradient is 0. In other words the tangent to the curve at that point is horizontal. The gradient of the curve can be expressed as dy/dx which is the first differential of the curve. dy/dx in effect gives us a formula to calculate the gradient of the curve at any x value. 2x^2+3x+4 differentiates to 4x+3. Since we know at the stationary point the gradient is 0 4x+3 must be equal to 0. Rearranging for x gives us x=-3/4 so the gradient of the curve is 0 at -3/4 and there is only 1 stationary point. To find the y coordinate substitute x=-3/4 into the original equation. y=2(-3/4)^2+3(-3/4)+4=23/8. This curve has 1 stationary point with coordinates (-3/4,23/8)
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