determining slope

Question

graph is y=4x^(1/3)

 

is the slope of the tangent line to the curve at x=a the negative of the slope of the tangent line to the curve at x=-a for any other values of a? explain

Answer 1

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

 

Whether you substitute a or -a in for x, in the denominator of the formula for y' you cube root of ±a, and then when you square that you get a^2/3 -- squaring will kill off any negativity.  So y'(±a) are identical.  Function is even, i.e.symmetric w.r.t. y-axis.