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Find the x coordinate of the stationary point of the following curves

  • #1

Homework Statement



Find dy/dx and determine the exact x coordinate of the stationary point for:

(a) y=(4x^2+1)^5

(b) y=x^2/lnx

Homework Equations




The Attempt at a Solution



(a) y=(4x^2+1)^5

dy/dx=40x(4x^2+1)^4

40x(4x^2+1)^4=0

Find x... How?

(b) y=x^2/lnx

dy/dx=2xlnx-x^2 1/x / (lnx)^2

2xlnx-x^2 1/x / (lnx)^2=0

Find x... How?
 

Answers and Replies

  • #2
993
13
40x(4x^2+1)^4=0

Find x... How?
re 1st prob:

Then either 40x = 0 or (4x^2+1)^4 = 0.

and solve the above two equations.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,804
931
You are aware that [itex]x^2/x= x[/itex] aren't you?

[itex]y= x^2/ln(x)[/itex]: [itex]y'= (2xln(x)- x)/(ln(x))^2= 0[/itex]
Use parentheses! What you wrote was [itex]y'= 2x ln(x)- (x/(ln(x))^2)= 0[/itex].

Multiply both sides of the equation by [itex](ln(x))^2[/itex]
and you are left with 2x ln(x)- x= x(2ln(x)- 1)= 0. Can you solve that?
 

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