Question

Suppose f (x) is a differentiable function such that f (1) = 7 and f ′(1) = 2. Use a tangent line approximation to estimate f (0.8).

Answer 1

Tangent approximation,

$f(x)=f(x_0)+f'(x_0)(x-x_0)$

$f(0.8)=f(1)+f'(1)(0.8-1)=7-2\cdot0.2=6.6$