5. What is the slope of the line tangent to the curve y3 – x2y + 6 = 0 at the point (1,-2)?
|
A. –(2/5) |
B. –(4/11) |
C. 4/11 |
|
D. 11/4 |
E. 8 |
Solution: The answer is B
Use the method of implicit differentiation. Since y is a function of x, take the derivative of both sides of the given equation with respect to x and apply the Chain Rule as follows:
Solve for dy/dx.
Where dy/dx is the slope of the line tangent to the given curve at any point (x,y).
Thus, the slope of the line tangent to the given curve at the point (1,-2) is obtained by substituting the corresponding x and y values into the above equation, as follows:
