Calculus Parabola Components of Line and Slope

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  According to definition, the slope of the tangent line to a function (parabola) is the first derivative of that function (parabola). We calculate the first derivative of the parabola. The derivative is y'=2x.

• Finding a maximum point of a function

  The x-intercepts are the roots of the quadratic equation: The roots are given by: The middle point is: In our case a=-2, b=140 thus: The solution shows how to find the location of a maximum point of a parabola using calculus and

• Shortest Length of Line Intersection

  First, the slope of L is So, we can get the slope of the normal line L' at P(a,b) as follows.

• Identify the type of graphs and its domain and range

  Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and the maximum number of riders possible.

• Tangent and velocity

  The equation of this tangent line can be written in the form y = mx + b? (1) Let the equation of the parabola be f(x) = x^2 + 3. The slope of the tangent at point (x1,y1) is f'(x1).

• Real-Life Applications of Hyperbolas and Parabolas

  Or you could say that the slope of the tangent line to the parabola at the point having any given x-coordinate will be greater than the slope of the tangent line to the hyperbola having the same given x-coordinate.

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  Assume the parabola and the tangent line intersects at (x0, y0), then y0=x0. (1) It also has . (2) , so at point (x0, y0), the slope is 2x0 for the tangent line.

• Applications of Parabolas and Hyperbolas: Real-Life Applications of Probability

  Or you could say, given the x-coordinate, the slope of the tangent line to the parabola at the point will be greater than the slope of the tangent line to the hyperbola. 1.

• line integral

  (3) Evaluate the given line integral, where C is the boundary of the region in the x-y plane enclosed by the parabola y = x^2 and the line y = 1, traversed in an anticlockwise direction.