Question

Consider the following function.

f(x) = x2 + 5, (1, 6)
(a) Find an equation of the tangent line to the graph of f at the given point.
y =

Answer 1

y = 2x +4

Explanation:

You want the equation of the tangent line to f(x) = x² +5 at the point (1, 6).

Slope

The slope of f(x) at x = 1 is its derivative at that point.

f'(x) = 2x

f'(1) = 2(1) = 2

Equation

The point-slope equation of a line is ...

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

We want a line with slope 2 through point (1, 6), so its equation will be ...

y -6 = 2(x -1)

In slope-intercept form, this is ...

y = 2x -2 +6

y = 2x +4 . . . . equation of tangent line

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