Let f(x)=4/√3x-2. Find the slope of the tangent line to the graph of f at the point (2, 2)

Question

Let f(x)=4/√3x-2.

Find the slope of the tangent line to the graph of f at the point (2, 2)

help please!!

Answer 1

First: your notation is only clear because you have specified that f passes through (2,2); otherwise the denominator is equivocal. You should use sqrt(...) to make clear what is under the radical sign.

f'(x) = 4 (-1/2) (3x-2)^-3/2 3 = -6/sqrt[(3x-2)³]

^{f'(2) = -6/sqrt(64) = -3/4}