Tangent to a curve

We can find the tangent to a curve using the derivative of the equation. During the 'Analytical geometry' course, a straight line equation was obtained by

where k is the slope and (x₀, y₀) is some point on the line.

Then the tangent equation at point a of the curve f(x) is obtained by

As the slope of the tangent in point a is the derivative of f(x) in point a

Example 1

Find the tangent to the function f when x = 3

The tangent when x = 3

The derivative of f and value of derivative when x = 3

The slope of the tangent is -8 and the value of the function at x = 3 is -5. This gives

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