A calculus problem by Playaof Reddevil

Calculus Level 2

Simple differential function

2 solutions

Playaof Reddevil
Sep 21, 2014

give y = x + 1

use "inverse property" ; x = y + 1

y = x - 1 and use x - 1 instead x to find f(x)

so f(x + 1) = f({x - 1} + 1) = f(x) = 2(x - 1)^2 - 1 = 2x^2 - 4x + 1

f'(x) = 4x - 4

so f'(6) = 4(6) - 4 = 20

Great! It is important to find the "actual function".

If we wanted to differentiate directly, we had to use the composite function theorem.

Calvin Lin Staff - 4 years, 5 months ago

Sam Sam
Dec 16, 2019

$f'(6) = f'(5+1)$

$\frac{d}{dx}(2x^{2}-1) = 4x$

$x = 5$

$4x = 20$