## Find derivative of f(x), plug in point to find slope. Slope of normal line is opposite reciprocal of this. Plug into y – y1 = m(x – x1).

### Find the equation of a line normal to f(x).

To find the derivative of a function f(x), we can use the power rule, product rule, quotient rule, and chain rule. The power rule is used when the function is in the form of xn, where n is any constant. The product rule is used when the function is the product of two functions. The quotient rule is used when the function is the quotient of two functions. The chain rule is used when the function is the composition of two functions.

Once we have found the derivative of f(x), we can plug in a point to find the slope of the tangent line at that point. The slope of the normal line is the opposite reciprocal of this slope.

To find the equation of the normal line at this point, we can use the point-slope formula, y – y1 = m(x – x1), where (x1, y1) is the point that we plugged in, and m is the slope of the normal line.

For example, let’s say we have the function f(x) = x^2 – 3x + 2. To find the derivative, we can use the power rule and the constant multiple rule:

f'(x) = 2x – 3

Let’s say we want to find the equation of the normal line at the point (2, 1). We can plug in x = 2 to find the slope of the tangent line:

f'(2) = 2(2) – 3 = 1

So the slope of the tangent line at (2, 1) is 1. The slope of the normal line is the opposite reciprocal of this, which is -1.

Now we can use the point-slope formula to find the equation of the normal line:

y – 1 = -1(x – 2)

Simplifying, we get:

y – 1 = -x + 2

y = -x + 3

So the equation of the normal line at the point (2, 1) is y = -x + 3.

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