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Find the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0.

A.
y = 2

B.
y = 2x

C.
y = 2x + 2

D.
y = –2x + 2

User Phreeskier
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1 Answer

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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:

User Mounarajan
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