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Quiz: Pre_Calculus Practice Quiz # 6

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Find the equation of the tangent line to k(x) = x + 2 at x = 1.
Write your answer in point-slope form using integers and fractions. Simplify any fractions.
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Answer 1

y = x + 2.

Explanation:

To find the equation of the tangent line to k(x) = x + 2 at x = 1, you can follow these steps:

1. Find the slope of the tangent line, which is equal to the derivative of the function k(x) at x = 1.

k(x) = x + 2

k'(x) is the derivative of k(x), which is simply 1 since the derivative of x is 1.

So, the slope of the tangent line at x = 1 is 1.

2. Now that you have the slope and a point (x = 1, k(1) = 1 + 2 = 3) on the curve, you can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is the point on the curve, and m is the slope.

Plugging in the values:

y - 3 = 1(x - 1)

Simplify:

y - 3 = x - 1

Now, isolate y:

y = x - 1 + 3

y = x + 2

So, the equation of the tangent line to k(x) = x + 2 at x = 1 is:

y = x + 2