Find the equation of the tangent line at (3,f(3)) when f(3) = 16 and f ' (3) = 3. (Use symbolic notation and fractions where needed.)

Question

Find the equation of the tangent line at (3,f(3)) when f(3) = 16 and f ' (3) = 3. (Use symbolic notation and fractions where needed.)

Answer 1

The formula for a tangent line is:

y - f(a) = f’(a) (x-a)

In our case we are given the point (3, f(3)).

We know f(3) = 16, f’(3) = 3 [the slope at said x value].

Now plug it in:

y - f(3) = f’(3) (x-3)

y -16 = 3 * (x - 3)

y = 3x +16 -9

y = 3x + 7

Tangent Line^

Feel free to correct me if something is off. Hope this helps.