Find the equation of the curve from the data given.

[SurnameLong]

5. Let m denote the slope of a curve as a function of x. Find the equation of the curve from the data given.
(a) dm/dx=-3 for all x; m=4 and y=-1 when x=-1
I integrated twice (-3x, -3/2x²) to get to (-3/2)x².
The answer is y=(-3/2)x²+x+(3/2). Other than (-3/2)x², I don't understand how x and the other 3/2 comes about.
Any help would be appreciated. Thanks.

 

[Ishuda]

5. Let m denote the slope of a curve as a function of x. Find the equation of the curve from the data given.
(a) dm/dx=-3 for all x; m=4 and y=-1 when x=-1
I integrated twice (-3x, -3/2x²) to get to (-3/2)x².
The answer is y=(-3/2)x²+x+(3/2). Other than (-3/2)x², I don't understand how x and the other 3/2 comes about.
Any help would be appreciated. Thanks.

You almost have it: Integrate once to get
m = -3 x + c
where c is the integration constant. Since m=4 when x=-1, what is c. After that
dy/dx = m
so integrate once and don't forget the constant of integration which you can find by noting that y=-1 when x=1.

 

[SurnameLong]

This helped alot.

(Thank you)²