Question

Estimate f′(−3) where f(x) = x^3 + 8x^2 − 10x − 1 to within one decimal place by using a small enough interval.
f′(−3) ≈

Answer 1

It is an estimation. You can use the first order approximations such as
f'(x) = (f(x+δ)-f(x))/δ

or a symmetrical formula, such as
(f(x+δ)-f(x-δ)/(2*δ)

δ can be a small number such as 0.1, 0.01,0.001,etc.