Math 16a worksheet 4 compute the derivative of fx 1radicx41

Question

MATH 16A WORKSHEET 4-

(1) Find all points P on the graph of f(x) = x³ - 4x such that the tangent line to f at P is perpendicular to y = x.

(2) Use limits to compute f'(1), where f(x) = x√x.

(3) Find a function f(x) and a real number a such that f'(a) = lim_h→0((2 + h)³ - 8/h), and find this limit by computing the derivative f'(x) and evaluating at x = a.

(4) Let f be the function defined as follows:

Draw a graph of f. Determine if f is continuous and/or differentiable at x = 0 and at x = 1.

(5) Compute the derivative of f(x) =1/√(x⁴+1) at x = 0.

(6) Find the equation of the tangent line to f(x) = 2/√(x-1) at x = 4.