Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:
Find the derivative of the function f(x) = 3x3 − x2 + 2
f'(x) = 9x^2 - 2x
Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point
f'(0) = 9(0)^2 - 2(0) = 0
Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.
y - f(a) = m(x - a)
y - (3*0^3 - 0^2 + 2) = 0(x - 0)
y - 2 = 0
So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:
y = 2
Therefore, the correct answer is A. y = 2
Explanation: