The function f whose graph passes through
(0,7/3) and whose derivative is x1−x2 isgiven by
f(x)=(1/3)1−x23/2+7
f(x)=(3/2)sin−1x+6
f(x)=−(1/3)1−x23/2−8
f(x)=−(2/3)1−x23/2−8
f(x)=∫x1−x2dx=−12∫(−2x)1−x2dx=−131−x23/2+C
So 7/3=−1/3+C⇒C=8/3
Therefore f(x)=−(1/3)1−x23/2−8