Consider the parabola y = 6x − x2. (a) find the slope of the tangent line to the parabola at the point (1, 5).

Given expression is

And we have to find the slope of the tangent line at the point (1,5), and for that, first we find the derivative of the given expression, which is

And the derivative is the slope. And to find the slope at point (1,5), we put 1 for x in the expression of derivative, that is

Hence, the slope of the tangent line to the parabola at the point (1, 5) is 4.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

2500

step-by-step explanation: