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: $y=\dfrac15 x +1$

Step-by-step explanation:

Since argument is the value of independent variable x .

Here y= 1 when x = 0.

$\dfrac{dy}{dx}=\dfrac15$

$\Rightarrow\ dy=\dfrac15 dx$

Taking integration on both sides , we get

$\int dy = \dfrac15 \int dx\\\\\Rightarrow\ y= \dfrac15 x +c$

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

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

Hence, the function will be

$y=\dfrac15 x +1$