Find two functions that this could be the derivative of:
y'=4x+7
Remember the derivative of any constant is zero.
take its antiderivative i suppose...
y= 2x^2 + 7x + any number
To find two functions that could be the derivative of y' = 4x + 7, we can integrate the given equation. Since the derivative of a constant is zero, the integration process involves finding the antiderivative of 4x and 7 separately.
Integrating the term 4x, we get:
∫4x dx = 2x^2 + C1,
where C1 is the constant of integration.
Similarly, integrating the term 7, we get:
∫7 dx = 7x + C2,
where C2 is another constant of integration.
Combining these results, we have two possible functions that could be the derivative of y' = 4x + 7:
1. y = 2x^2 + 7x + C1, where C1 is any constant.
2. y = 2x^2 + 7x + C2, where C2 is any constant.
So, by integrating the given equation, we found two functions that could potentially have y' = 4x + 7 as their derivative.