What have you done so far? Do you know anything about related rates? Start by differentiating, then use the fact that:mattsoto said:A point moves along the curve y=2x^2+1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x=(3/2)?
The equation for the curve y=2x^2+1 is a quadratic function that represents a parabola with a vertical stretch of 2 and a horizontal shift of 1 unit to the right.
The coordinates of a point moving along the curve y=2x^2+1 can be found by choosing a value for x and plugging it into the equation to solve for y. For example, if x=3, then the coordinates of the point would be (3,19).
Yes, the curve y=2x^2+1 is symmetrical about the y-axis. This means that if you were to fold the graph in half along the y-axis, the two sides would overlap perfectly.
The slope of the tangent line to the curve y=2x^2+1 at a given point can be found by taking the derivative of the equation, which is 4x. Then, plug in the x-coordinate of the given point to find the slope.
The coefficient 2 in the equation y=2x^2+1 affects the curve by determining the steepness of the parabola. A larger coefficient results in a narrower and steeper curve, while a smaller coefficient creates a wider and less steep curve.