Wednesday

October 1, 2014

October 1, 2014

Posted by **Ivan** on Thursday, November 6, 2008 at 8:27pm.

- Calculus -
**Reiny**, Thursday, November 6, 2008 at 8:53pmlet the point of contact in the first quadrant be P(a,b) or P(a,1-a^2)

slope of the tangent is -2x (the derivative)

so at P the slope is -2a

equation of the tangent is

(y - (1-a^2))/(x-a) = -2a

which simplifies to

2ax + y = a^2 + 1

the base of the triangle will be the x-intercept of the tangent

the height of the triangle will be the y-intercept of the tangent.

x-intercept : let y = 0, then x = (a^2+1)/(2a)

y-intercept : let x = 0, then y = a^2 + 1

so the Area = (a^2 + 1)^2 /(4a)

use the quotient rule to find the derivative of Area, set that equal to zero and solve.

let me know what you got.

**Answer this Question**

**Related Questions**

calculus - Find the x-coordinate of the point P on the parabola y=1-x^2 (0<x...

math - A tangent line is drawn to the hyerbola xy=c at a point P. 1) show that ...

math repost!! - please help, i procrastinated and now this is due tomorrow!! A ...

Calculus 151 - At what point in the first quadrant on the parabola y=4-x^2 does ...

Calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...

calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...

Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...

calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...

calculus - Find the area of the region in the first quadrant enclosed by the ...

calculus - Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) ...