**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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