Derivatives : Point of Horizontal Tangent and Derivative at a Point

Consider the curve given by x^2+4y^2 = 7 + 3xy

a) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P.

b) Find the value of d^2*y/d*x^2 at the point P found in part a).

Solution Summary

The Point of a Horizontal Tangent and Derivative at a Point are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... solutions to some questions on finding derivatives, slope of ... Then find the value of the derivative as specified. ... Find the point where the graph of the function ...

... b) The second derivative helps us to find the intervals of ... c) Use the graph to find the point on the graph where the curve crosses the horizontal asymptote ...

Graphs and Derivatives. ... the tangent lines to the graph at some more points, you can ... the function, then this function is decreasing, and the derivative should be ...

... the point is , − where the tangent line is horizontal. ... b) The critical points happens when ... 2 According to second derivative test, y '' = − < 0 , so ...

Applications of the Derivative. ... ii) Find the equation of the normal line at the point (5, 4 ... 2. A ladder 10 m long rests on horizontal ground and leans against a ...

... 2. Find the derivatives (dy/dx) of the following functions. ... line using the definition of the derivative to the ... Then find the points on the function where the ...

... The latus rectum is the length of the horizontal line segment ...tangent line to the curve, we need a point and the ... The slope is the derivative of y taken as an ...

... In the horizontal direction, since there is no motion, Newton's second law ...tangent of the angles is the value o the derivative at that point with respect to ...

... Making use of the horizontal tension components ... where and are derivatives of the two function with ... of wave crests originating from the intersection points A and ...