# How do you find the slope of the tangent line to the graph at given point and give an equation of the tangent line #f(x)=3/2x# at (1, 3/2)?

The answer may seem strange when compared to what we know about tangent lines to circles and other curves. Please see below.

If we want the details:

The slope of the tangent line is given by

So we have

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To find the slope of the tangent line to the graph at a given point, we can use the derivative of the function. The derivative of f(x) = 3/2x is f'(x) = 3/2.

The slope of the tangent line is equal to the derivative evaluated at the x-coordinate of the given point. In this case, the x-coordinate is 1. So, the slope of the tangent line is 3/2.

To find the equation of the tangent line, we can use the point-slope form of a line. The equation is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Plugging in the values, we have y - 3/2 = (3/2)(x - 1). Simplifying this equation gives y = 3/2x - 3/2 + 3/2, which simplifies further to y = 3/2x.

Therefore, the equation of the tangent line to the graph f(x) = 3/2x at the point (1, 3/2) is y = 3/2x.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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