Question

if f(x)=|x-2020|, then f'(x) at x=2019 is given by

a) 1

B)-1

C)0

D)2019
(correct option is -1)

Answer 1

Answer:

D.

Step-by-step explanation:

x=2019

f(x)=lx-2020l

=l 2019-2020l

= l-1l

Answer 2

The correct answer is option (b). -1.

Given:

$f(x)=|x-2020|$.

To Find:

We have to find out the value of $f'(x)$ at $x=2019$.

Solution:

Given that, $f(x)=|x-2020|.$

$i.e., f(x) = x-2020,$ if $x\geq 2020$

and $f(x) = -(x-2020),$ if $x < 2020.$

If $x=2019,$ the value of x is less than 2020.

∴, $f(x) = -(x-2020)$.

Now, the derivative of above function,

$f'(x) = \frac{d}{dx} ( -(x-2020)) = -1.$

∴, At $x=2019,$

$f'(2019) = -1.$

Hence, the value of $f'(x)$ at $x=2019$ is -1.

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