Tangent line
= Tangent line
{title2=$y=f(a)+f'(a)(x-a)$}
The <tangent line> to a differentiable <function> at $a$ is its affine first-order approximation $f(a)+f'(a)(x-a)$. For a differentiable <concave function>, it is an upper bound throughout a convex interval: the secant-slope inequality and passage to the <derivative> give $f(x)\leq f(a)+f'(a)(x-a)$. This upper bound constructs valid envelopes in <adaptive rejection sampling>.