Question

For the function f: R ->R,f(x) = 7 - " align="absmiddle" class="latex-formula"> , find:
f' (-1).Show all working

Answer 1

Answer:

$f'(-1) = \pm 2\sqrt{2}$

Step-by-step explanation:

For $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(x) = 7-x^2$, find $f'(-1)$

Recall that

$f'(y)=x \text{ whenever } f(x) = y, \forall y \in \mathbb{R}$

Therefore,

$f(x) = 7-x^2 \implies y = 7-x^2 \implies x = 7-y^2 \implies y = \pm \sqrt{ 7-x}$

$\therefore f'(x) = \pm \sqrt{ 7-x}$

$f'(-1) = \pm \sqrt{ 7-(-1)} = \pm \sqrt{8} = \pm \sqrt{2^3 } = \pm 2\sqrt{2}$