Find the value of x where the tangent is horizontal for

recall that a tangent line that's horizontal has a slope of 0 and the value of "x" is simply the critical points.

one may note that we can get two more critical points from zeroing out the denominator, but those critical points are usually asymptotic and the equation is not differentiable at those points.

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3

1st part is 64,000,000

2nd part 500,000

step-by-step explanation: