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To write the equation of the tangent line, you need a point (that's given) and the slope. dy/dx is the formula for the slope at any value of x.

The substitute 1.2 for x in the tangent line equation.
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First, we need to find dy/dx at the point (1, 0). To do this, we simply plug in the values for x and y into the equation for dy/dx, getting:

dy/dx = e^0 × (3(1)^2 - 6(1)) = 1(-3) = -3

Then, to find the tangent line, we use the formula:

y - y1 = m(x - x1)

Plugging in 0 for y1, 1 for x1, and -3 for m, we get:

y - 0 = -3(x - 1)

Therefore:

y = -3x + 3

Now, to approximate f(1.2), we say that the tangent line approximates the function. Therefore, we would say that when x is close to 1:

 f(x) ~ -3x + 3

Then, we simply plug in 1.2 and get:

f(1.2) ~ -3(1.2) + 3 = -3.6 + 3 = -0.6

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