Question

Let F (x) = 2^x. Which of the following represents the difference quotient with h = 0.001 which can be used to estimate F '(3)?

Answer 1

Maybe: \(\dfrac{2^{3.001} + 2^3}{0.001}\)?

Answer 2

Whoops! Minus, not Plus. \(\dfrac{2^{3.001} - 2^{3}}{0.001}\). Sorry about that.

Answer 3

later on you will know it is \(2^3\times \ln(2)\)

Answer 4

note that
\[\frac{2^{3.001}-2^3}{.001}=2^3\left(\frac{2^.001-1}{.001}\right)\] by the laws of exponents

Answer 5

Thank you!