SOLUTION: I'm having trouble with this calculus problem: find the slope of the tangent line of x^2/3 + y^2/3 = 4 at the point (-1,3 sqrt3) Thank you

Question 683247: I'm having trouble with this calculus problem:
find the slope of the tangent line of x^2/3 + y^2/3 = 4 at the point (-1,3 sqrt3)
Thank you
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Rewrite the equation to isolate y on the LHS:
y^(2/3) = 4 - x^(2/3)
y = (4 - x^(2/3))^(3/2)
The slope of the tangent line is the derivative, dy/dx at the point x=-1:
dy/dx(x=1) = (3/2)(4-x^(2/3))^(1/2)*(-2/3)(x^(-1/3) = -(4-x^(2/3))^(1/2)/x^(1/3) = -(4-1)^1/2/-1 = sqrt(3) = 1.7321
RELATED QUESTIONS
I'm having trouble starting this calculus problem: Find the slope of the tangent line... (answered by Alan3354)

I'm having a little trouble with this question. Line 1: 3/4x+1 Line 2: (3,1) a.... (answered by Alan3354)

Find the equation of the tangent at the point (0,3) on a circle of x sqr + y sqr =... (answered by Alan3354)

Calculus Question Determine the equation of the line tangent to the graph of {{{... (answered by solver91311)

Please solve 1. Let m(x) be the slope of the tangent line to the curve y = x^3 - 2x^2 +... (answered by Alan3354,stanbon)

Need help with this problem please. Find the equation of the line that contains the... (answered by ankor@dixie-net.com)

find the slope and equation of the tangent line to y=x^4-5x^3+2 at... (answered by josgarithmetic)

Find the slope of the tangent line to the graph of the function at the given point.... (answered by jim_thompson5910)

what the slope of the tangent line of the curve x^2-xy+y^2=3 at a point... (answered by ikleyn)