Yay, implicit differnentiation
when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx
for x, the dy/dx dissapears
ok
so differnetiate and solve for dy/dx
3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)
so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
dy/dx=2/5
answer is 2/5
The number of solutions of a quadratic equation
ax^2+bx+c=0
Depends on its discriminant
/Delta=b^2-4ac
If /Delta>0 there are two distinct solutions
If /Delta=0 there are two coincident solutions
If /Delta<0 there are no solutions.
We know that there are two real solutions (I assume you mean distinct solutions), so we know that the discriminant is positive:
The number of solutions of a quadratic equation
Depends on its discriminant
If there are two distinct solutions
If there are two coincident solutions
If there are no solutions.
We know that there are two real solutions (I assume you mean distinct solutions), so we know that the discriminant is positive:
b^2-4ac=9+28t>0\iff t>-\dfrac[9][28]
Youre answer is D, you’re welcome
