Posted by **TG** on Friday, February 10, 2012 at 11:12pm.

Find the positive value of x where fx=x3+2x1/3 has a horizontal tangent line.

Answer =

- Calculus -
**Reiny**, Friday, February 10, 2012 at 11:54pm
I will assume you meant:

f(x) = x^3 + 2x^(1/3)

then f'(x) = 3x^2 + (2/3)x^(-2/3)

for a horizontal tangent, f'(x) = 0

3x^2 + (2/3)/(x^(2/3)) = 0

multiply by x(2/3)

3x^(8/3) = -2/3

x^(8/3) = -2/9

x = (-2/9)^(3/8) , which is undefined (can't take an even root of a negative)

Unless you typed something different from what I assumed, there is no horizontal tangent.

see

http://www.wolframalpha.com/input/?i=x%5E3+%2B+2x%5E%281%2F3%29

## Answer this Question

## Related Questions

- Calculus-derivatives - Verify these answers~ 1. For what value(s) of x does f(x...
- calculus - Consider line segments which are tangent to a point on the right half...
- Calculus - Given the function y=(x^2-5/x+3), answer the following questions. a) ...
- calculus - find the points on a graph of f where the tangent line is horizontal...
- Calculus - Find the points on the graph of f where the tangent line is ...
- math - question: find the points at which the graph of x^2 -4x + y62 -6y =12 has...
- Geometry Multiple Choice Question Please Help! - Find the value of x. If ...
- GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION - Find the value of x. If ...
- Calculus Need of Urgent Assistance - Let f(x) = x3 − 7x2. Find the point(s...
- ap calculus ab - for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) ...