Determine the slope of the tangent to the curve...

Question

Determine the slope of the tangent to the curve f(x) = -4v^3 + (3/x) +√x -2 at x=1

Answer 1

Find slope of f(x) = -4x^3 + 3/x +√(x) - 2 at x = 1

 

f(x) = -4x^3 + 3x^(-1) + x^(1/2) - 2

 

f '(x) = -12x^2 - 3x^(-2) + (1/2)x^(-1/2)

 

f '(1) = -12 - 3 + 1/2 = -14 1/2 = -14.5