Math Is Fun Forum

Given function is f(x) = 2/(x+1).
We need to find the equation of the tangent at (0, 2)

Step 1: Find the derivative of the function f(x) = 2/(x + 1)
f1(x) = -2/(x+1)^2 = -2/(x^2+2x+1)
Step 2: Now, substitute the x value from the given point in the derivative of f(x) and find the slope of the required line.
==> -2/(0 + 0 + 1)
f1(x) = -2.
==> Slope = -2.
Step 3: Now, we have the slope as -2 and the point as (0, 2).
then the equation is given by y - y1 = m(x-x1)
y -2 = -2(x-0)
y - 2 = -2x
==> 2x + y - 2 = 0 is the required equation of the tangent.

Yes... Thanks for the nice explanation John

You are most welcome  natasha..... :-)

Initially, the shrub was 20 cm high.. the very first month.. its growing 8cm and the second month 4 cm and the third month 2 cm..

And this pattern is continuing. so the fourth month the height will increase 1 cm and the in the fifth month the height will increase 1/2cm and in the sixth month it will increase by 1/4 cm.. and so on..

so..  20 + 8+4+2+1+(1/2) + (1/4) + so on...

35 +  very small number.

You are most welcome baker:)

So, The number of visitors in the year 2002 is 44,800..

Have you got it?

Sorry the fourth option.. 44,800

Natashabaker , The answer for the first question given by you is the third option.. 44, 800...