Find two functions that this could be the derivative of:
y'=4x+7
I have one: y=2x^2 + 7x
I cant think of another one!!
add a constant.
Remember that you can add an arbitrary constant to any integral. The derivative will be the same.
To find another function whose derivative is y' = 4x + 7, you can take the integral of the given expression.
Integrating the equation y' = 4x + 7 with respect to x will yield the original function y, up to an arbitrary constant of integration.
Integrating 4x + 7 with respect to x, we get:
y = 2x^2 + 7x + C
where C is the constant of integration.
This is the same function you had mentioned: y = 2x^2 + 7x.
By adding a constant C, you can obtain various functions that satisfy the given derivative.
For example, if C = 1, then y = 2x^2 + 7x + 1 is another function whose derivative is y' = 4x + 7.
In general, you can choose any constant C and it will result in a different but valid function that has the same derivative.