Question

For what values of x is the line tangent to the graph of f(x) = 4sqrtx-2x parallel to the x-axis?

For what values of x is the line tangent to the graph of f(x) = 4sqrtx-2x parallel to the y-axis?

Answer 1

steps below

Explanation:

f(x) = 4√x - 2x ... x≥0

f'(x) = 2/√x - 2

critical points: x=0, x=1

x=1 y = 4√1 -2x1 = 2

extreme: (1,2) tangent line parallel to x axis: y = 2 .... x = 1

x = 0 (x≥0): (0,0) tangent line parallel to y axis: x = 0