Question

Find the x coordinate of the point, correct to two decimal places, on the parabola y=6.17-x^2 at which the tangent line cuts from the first quadrant the triangle with the smallest area.

Answer #1

Consider the graph of y=f(x)=1−x2 and a
typical point P on the graph in the first quadrant. The tangent
line to the graph at P will determine a right triangle in the first
quadrant, as pictured below.
a) Find the formula for a function A(x) that computes the area
of the triangle through the point P=(x,y)
b) Find the point P so that the area of the triangle is as small
as possible: P =()

Let f(x)=x^2 Find the first coordinate of the intersection point
of the two tangent lines of f at 1 and at 5.

USING ITERATED INTEGRALS, find the area bounded by the
circle x^2 + y^2 = 25,
a.) the x-axis and the parabola x^2 − 2x = y
b.) y-axis and the parabola y = 6x − x^2
b.) (first quadrant area) the y-axis and the parabola x^2 − 2x =
y

a. Draw the parabola y=x^2 and the point (0,3) in the square
window -2 < x < 2 and 0 < y <4.
b. Fill in the four blanks to complete the formula
giving the distance D from the point (0,3) to a general point (x,y)
in the plane.
D = Sqrt[( - )^2 + ( - )^2]
c. Find the points on the parabola y=x^2 which are closest to the
point (0,3). You must have both appropriate calculations...

The x-coordinate of the centroid of area in the first quadrant
bounded by y =1 - x^2 and coordinate axes is

Find the point with x ≥ 0 on the parabola y = (1/8)x^2 − 5 that
is closest to the point ( 0 , 1 ).

let
P be the point on the line y=4.65x+4.18 which is closest to the
orgin. find the x-coordinate of P correct to two decimal
places

Write a program to check the location of a point (x, y) in a 2D
coordinate system and display message differently: point (x, y) is
on the original point; or is on the x-axle; or on the y-axle; or in
one of 4 quadrants. When the point (x, y) is in a quadrant, the
message should include quadrant information. For example, point (3,
5) is in quadrant I.
In Java Please

Find the slope of the line tangent to the curve y=x^2 at the
point (-0.9,0.81) and then find the corresponding equation of the
tangent line.
Find the slope of the line tangent to the curve y=x^2 at the
point (6/7, 36,49) and then find the corresponding equation to the
tangent line.
answer must be simplified fraction

Find an equation for the line tangent to the parabola y= 2x^2
-13x +5 which has a slope of -1

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