Approximate the following value using derivatives (without a calculator)

Question

(1.1)^4 - (1.1)^2

I only know how to do linear approximation when using square roots. How do I do this type of problem?

Answer 1

The final answer would be 1.21

First subtract:
(1.1^4) - (1.1^2) = 1.1^2
then solve:
(1.1)^2 = 1.21

How it works:

If you have x^4 - x^2 and the value of x is the same, just subtract the exponents. x^4 - x^2 = x^2

Google search exponent and go to mathisfun for more info and practice.

In this case 1.1^4 is just 1.1 * 1.1 * 1.1 * 1.1
so you can subtract 1.1^2 which is 1.1 * 1.1 from that, and get 1.1 * 1.1 .
1.1 * 1.1 = 1.21

Good Luck!

Answer 2

P.S. Can't edit here..

The exponent of a number says how many times to use the number in a multiplication of itself.