Find an equation of the line tangent to at x = 3.

Question

Find an equation of the line tangent to  at x = 3.

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to take the derivative of the function and evaluate it at x = 3. Using the power rule, we get:

f'(x) = 2x - 6

Evaluated at x = 3, we have:

f'(3) = 6 - 6 = 0

This means that the slope of the tangent line is 0. To find the y-intercept of the tangent line, we need to find the y-coordinate of the point on the original function where x = 3. Plugging x = 3 into the function, we get:

f(3) = 2(3)^2 - 6(3) + 5 = 2

Therefore, the equation of the tangent line is y = 2, which can be written as:

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Find an Equation of the Line Tangent to at X