Find the equation of the tangent to the parabola. 1.
at (3/2 , 6)

2.
at (6,3)

Step-by-step explanation:

The slope of the line is dy/dx. That can be found by differentiation, implicit or otherwise.

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Implicit differentiation:

  2y·dy = 24·dx

  dy/dx = 24/(2y) = 24/(2·6) = 2 . . . . . at y=6

Then the point-slope equation of the tangent is ...

  y -6 = 2(x -3/2)

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Straight differentiation:

  2x = 12·dy/dx

  dy/dx = x/6 = 6/6 = 1 . . . . . at x=6

Then the point-slope equation of the tangent is ...

  y -3 = x -6

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Additional comment

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

Here, m = dy/dx. (h, k) is the given point of tangency.

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17