Find dy/dx at the point (-3, 1) for the equation x = y^3-9y^2+5.
A. -1/17
B. -1/13
C. -1/15
D. 1/17
E. 1/15
I posted this question before with a typo, but the point still doesn't appear to be on the graph of the function.
yes it is. Perhaps you are misled by the x being the independent variable instead of y
When y = 1
x = 1^3 = 9 (1)^2 + 5
= 1 - 9 + 5
= -3 sure enough
now the problem
dx/dx = 1 = 3 y^2 dy/dx - 18y dy/dx
1 = (3y^2-18y)dy/dx
dy/dx = 1/ (3*1^2 -18*1)
dy/dx = 1/(-15) = -1/15
amazing - that is one of the choices !
Sometimes conventional obscurity is insufficient and extraordinary efforts must be made to confuse the student. One seemingly simple but surprisingly effective technique is to reverse the usual roles of x and y.
Haha! Thank you!
You are welcome.
To find dy/dx at a specific point for the given equation, you can use implicit differentiation.
The equation given is x = y^3 - 9y^2 + 5. We want to find dy/dx when x = -3 and y = 1.
First, differentiate both sides of the equation with respect to x:
d/dx(x) = d/dx(y^3 - 9y^2 + 5)
Since x is not a function of y, its derivative with respect to x will be 1. For the right side of the equation, we need to apply the chain rule.
1 = 3y^2(dy/dx) - 18y(dy/dx)
Now we can rearrange the equation to solve for dy/dx:
1 + 18y(dy/dx) = 3y^2(dy/dx)
Factor out dy/dx:
(18y - 3y^2)(dy/dx) = -1
Now substitute the given values, x = -3 and y = 1, into the equation:
(18(1) - 3(1^2))(dy/dx) = -1
15(dy/dx) = -1
Finally, divide both sides by 15 to isolate dy/dx:
dy/dx = -1/15
Therefore, the answer is C. -1/15.