Find the slope of the function (which is the slope of the tangent line to the graph of the function) y = x² + 2x + 3 at the point x = 1

Solution:

Given, the function is y = x² + 2x + 3

The point is x = 1.

We have to find the slope of the function.

At x = 1,

y(1) = (1)² + 2(1) + 3

y(1) = 1 + 2 + 3

y(1) = 6

The point on the curve is (1, 6).

On differentiating,

dy/dx = 2x + 2

At x = 1,

dy/dx = 2(1) + 2

= 2 + 2

= 4

Therefore, the slope of the function is 4.

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Find the slope of the function (which is the slope of the tangent line to the graph of the function) y = x² + 2x + 3 at the point x = 1

Summary:

The slope of the function (which is the slope of the tangent line to the graph of the function) y = x² + 2x + 3 at the point x = 1 is 4.