equation of line

Question

the question is find an equation to the line that is tangent to f(x)=sqrt of  x^6 and is parralel to the line 6x-2y+10=0. Please help thank you

Answer 1

f(x) =sqrt(x^6) = x^3

f'(x) = 3x^2

Also, 6x - 2y +10 =0

or 2y = 6x +10

or y = 3 x +5, 

Since, tangent from f(x) is parallel to the line 6x - 2y +10 =0, so

3x^2 = 3

x^2 = 1

x = +/- 1

x = 1 or -1

then f(1) = 1 and f(-1) = -1

So the equation of line will be

y-1 = 3(x-1)  if f(1) or

y+1 = 3(x+1) if f(-1)