Limits, Continuity: triangle is created by y-axis, x-axis, and tangent to f(x)=2/x...

[Alexandria1101]

Please if someone could help me with this question, I don't know where I should start.
triangle is created by the y-axis, the x-axis and the tangent to f(x)=2/x. Show that the area of this triangle is constant.

 

[Deleted member 4993]

Please if someone could help me with this question, I don't know where I should start.
triangle is created by the y-axis, the x-axis and the tangent to f(x)=2/x. Show that the area of this triangle is constant.

First of all - make a sketch.

 

[stapel]

Please if someone could help me with this question, I don't know where I should start.
triangle is created by the y-axis, the x-axis and the tangent to f(x)=2/x. Show that the area of this triangle is constant.

After you've done the drawing, think about the formula for the area A of a triangle, given the base b and the height h. How might you relate this formula to the x- and y-axes? Given that the third side (which cuts the x- and y-axes to form the base and the height) is tangent to f(x) = 2/x, what then must the slope of the tangent be, for a given value of x? And so forth.

If you bog down, please reply showing all of your steps and reasoning. Thank you!

 

[SAMUELK]

Please if someone could help me with this question, I don't know where I should start.
triangle is created by the y-axis, the x-axis and the tangent to f(x)=2/x. Show that the area of this triangle is constant.

And:
Second of all: Pick a point x0. Derive the EQUATION of the line tangent to y = 2/x at x = x0.

Third: Find the y-intercept of that line. Then find the x-intercept.

Them's your base and height.

 

[pka]

Please if someone could help me with this question, I don't know where I should start.
triangle is created by the y-axis, the x-axis and the tangent to f(x)=2/x. Show that the area of this triangle is constant.

Suppose that $\displaystyle \left( {a,\frac{2}{a}} \right),~a>0$ is a point on the graph of $\displaystyle y=\left( {\frac{2}{x}} \right)$

Now $\displaystyle y - \frac{2}{a} = \frac{{ - 2}}{{{a^2}}}\left( {x - a} \right)$ is the line tangent to the graph at that point. The $\displaystyle x~\&~y$ intercepts are the acute vertices of the triangle the area of which you are asked to show is a constant independent of $\displaystyle a$.