Finding coordinates

Question

Find the coordinates of the points, if any, where each functions has a horizontal tangent line.

a) f(x)= 2x-5x^2

b) f(x)= x^3-8x^2+3

Answer 1

A) I will give you the first one, and have you try the second. Finding horizontal tangent lines requires only that you find the derivative, then set to "horizontal", i.e. zero. The function needs nothing worse than a power rule, which means you get...

   2 - 10X = 0

   2 = 10X

   1  = X

   5

Plug into the original function to get:

2 ( 1 ) - 5 ( 1 )²

     5           5

2  -  5   =  1                 So A has one solution: (1/5 , 1/5)

 5   25       5

 

B is a little more work because you will get a polynomial when you derive, but you can do it.