Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Families of functions

Consider the function with the rule

. Find the equation of the tangent of the curve y = f(x) at the point where

.

aaaah I can't get my head around this! The solution skips a lot of steps, so I find it hard to follow, can someone help me please?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Families of functions

Note that if

then

while if

then

.

Hence

for

.

Last edited by JaneFairfax (2008-07-13 02:30:43)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Families of functions

Right, here’s a geometric interpretation.

The curve

has the following shape:

It’s a curve with two downward-pointing prongs, the tips of the prongs being

and

. When a > 0, the

prong is to the right of the origin; When a < 0, it’s to the left of the origin. In either case, the maximum point is at

, and the point at

is always between the origin and the maximum point.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Families of functions

Oh ok, I think I get it, thanks JaneFairfax!

Is the answer

?

Last edited by Identity (2008-07-13 04:54:55)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Families of functions

Looks good to me.