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The function y=3x2 4x−2 has a horizontal tangent at : a.

a. (−2,6)
b. (0,−2)
c. (−1,−3)
d. (−2/3,y)

1 Answer

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Final answer:

The function y=3x^2+4x-2 has a horizontal tangent at the point (-2/3, -14/3), which corresponds to option d. after calculating the y-coordinate using the function.

Step-by-step explanation:

The function given is y = 3x^2 + 4x - 2. To find where the function has a horizontal tangent, we look for points where the derivative of the function is equal to zero. The derivative of y with respect to x is dy/dx = 6x + 4. Setting the derivative to zero gives us:

0 = 6x + 4

x = -4/6

x = -2/3

Substituting x = -2/3 into the original function to find the y-coordinate:

y = 3(-2/3) ^2 + 4(-2/3) - 2

y = 3(4/9) - 8/3 - 2

y = 4/3 - 8/3 - 2

y = -12/3 + 4/3 - 6/3

y = -14/3

Thus, the function has a horizontal tangent at the point (-2/3, -14/3), matching option d. with the correct y-value filled in.

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