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(x1)+f'(x1)(x-x1)

Then,

f(x)=f(1)+f'(1)(x-1)=7+2(x-1)

And,

f(0.8)=6.6