A function is 1 when its argument is zero. Its value is 1/5 its slope at any point. What is the function?

Question

asked Sep 12, 2022 73.8k views

1 Answer

Magdeline · Answer 1 · 2022-09-17T05:11:16+0000

Answer:
$y=\frac15 x +1$

Explanation:

Since argument is the value of independent variable x .

Here y= 1 when x = 0.

$(dy)/(dx)=\frac15$

$\Rightarrow\ dy=\frac15 dx$

Taking integration on both sides , we get

$\int dy = \frac15 \int dx\\\\\Rightarrow\ y= \frac15 x +c$

Put y=1 and x=0 [given] , then

$1= 0+c\\\\\Rightarrow\ c=1$

Hence, the function will be

$y=\frac15 x +1$