Question

find critical pts. of 4/x+x^4

Answer 1

To find critical points,we take the derivative of the function. do you know how to take the derivative?

Answer 2

yes

Answer 3

i get x=1

Answer 4

Lets see...

Answer 5

ok try this find dy/dx of ylnx=e^1-x+y^3 at x=1

Answer 6

i would make a common denominator of the function to evaluate it.\[\large f(x) = \frac{4}{x} +x^4\]\[\large f'(x) = \left(- \frac{4}{x^2}\right)+4x^3 =0\]\[\large -\frac{4}{x^2} +4x^3 \cdot \frac{x^2}{x^2} = 0\]\[\large -\frac{4}{x^2} + \frac{4x^5}{x^2} =0\]\[\large \frac{4x^5-4}{x^2}=0\] there are variables in the numerator and denominator,so set both = 0 and solve \[\large 4x^5 - 4 = 0\]\[\large x^2 = 0\]

Answer 7

You can also check your solutions by plugging them back into derivative to see if they =0.

Answer 8

Sorry, just equate your numerator to 0, not your denominator.

Answer 9

So you are right. x=1.

Answer 10

\[\large f'(1) = -\frac{4}{(1)^2}+4(1) = -4+4=0\]