Question

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

Answer 1

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`