For the​ function, find the points on the graph at which the tangent line is horizontal. If none​ exist, state that fact. SHOW WORK PLEASE!

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  A. (-√2, 3+(4√2)/3), (√2, 3-(4√2)/3)

Step-by-step explanation:

The tangents are horizontal where the derivative is zero. The derivative of the given function is ...

  y' = x² -2

This is zero when ...

  0 = x² -2

  2 = x²

  ±√2 = x . . . . x-values where the derivative is zero

__

The corresponding y-values are ...

  y = (1/3x² -2)x +3

  y = (1/3(2) -2)(±√2) +3 = 3 ∓ (4√2)/3

The turning points are (-√2, 3+(4√2)/3) and (√2, 3-(4√2)/3).

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared