Finding the equation of a tangent line

The tangent touches the graph at x₀ and has the same slope there. The derivative gives the slope, the point gives the intercept.

Rules

Three problems on this topic. Type like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x).

Task 1 of 3Tangent lines

Task

Find the tangent to

f (x) = - x^{3} + x^{2} + 2 x + 4

x_{0} = 0

in the form

t (x) = m x + b

Slope $m$

Intercept $b$

Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

Worked example

Find the tangent to $f (x) = - x^{3} - 2 x^{2} - 2 x$ at $x_{0} = - 2$ in the form $t (x) = m x + b$ .

Worked solution

Typical mistake: Using the function value $f (x_{0})$ instead of the derivative $f^{'} (x_{0})$ as the slope.

Common questions

The normal is perpendicular to the tangent. Its slope is −1/m.