equation of tangent

Question

write an eqaution of tangent to each curve at the given point

p (1,-1)

y= √x - 2/^3√x                    (cubic root of x)

Answer 1

I assume the equation for y is

 

y = √x - 2x^-1/3

 

y' = (1/2)x^-1/2 - 2(-1/3)x^-4/3

 

m = y'(1) = (1/2)1^-1/2 - 2(-1/3)1^-4/3 = 1/2 + 2/3 = 7/6

 

y = mx + b = (7/6)x + b

 

At (1,-1),

 

-1 = (7/6)1 + b

 

b = -13/6

 

y = (7/6)x - 13/6