Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 55

Eliminate the radical by rewriting it as a fraction.
The function becomes:
f(x) = 2/ (x^3)^(1/4) = 2/x^(3/4) = 2x^(-3/4)
Take the derivative by using the power rule.
f'(x) = -3/4 (2)(x^(-3/4-1))
f'(x) = -3/2 (x^(-7/4))
f'(x) = -3/(2x^(7/4))
Substitute x=1.
f'(1) = -3/(2(1)^(7/4)) = -3/2
With the slope of the point, and the given point (1,2), use the slope intercept form to find the equation.
y=mx+b
2=(-3/2)(1)+b
2+3/2=b
b=7/2
The equation of the tangent line is:
y= -3/2 x +7/2
Graph both the equation of the tangent line with the original function. They should intersect at (1,2).
See the image attached.