Question

Can anyone explain (step-by-step) how to work out this calculus problem?

Answer 1

Explanation:

Use the difference quotient

`(f(x + h) - f(x))/(h)`

Here it will become

`\frac{2 (0.85) {}^(x + h) - 2(0.85 {}^(x)) }{h}`

For the first box, let x=-4, and h= 0.001

`\frac{2(0.85) {}^( - 4 + 0.001) - 2(0.85) {}^( - 4) }{0.001}`

Using a calculator, you will get about

`- 0.622`

Next, let do this for 0.5

`\frac{2(0.85) {}^(0.5 + 0.001) - 2(0.85) {}^(0.5) }{0.001}`

You will get about

`- 0.3`

Finally, do this for

1.25

`\frac{2(0.85) {}^(1.25 + 0.001) - 2(0.85) {}^(1.25) }{0.001}`

You get about

`- 0.265`

Note : This is the definition of a derivative