Question

Differentiate Implicitly To Find The Slope Of The Curve At The Given Point. x²+3y² =13;(1,2)

A) -6
B) 6
C) −6/1
D) 6/1

Answer 1

To find the slope of the curve at the given point, differentiate the equation implicitly and solve for the derivative. The slope of the curve at the point (1, 2) is -1/6.

Step-by-step explanation:

To find the slope of the curve at the given point, we need to differentiate implicitly. Differentiating the equation x²+3y²=13 with respect to x gives 2x + 6yy' = 0, where y' represents the derivative of y with respect to x.

Now, we can substitute the given point (1, 2) into the equation and solve for y'. Substituting x = 1 and y = 2, we get 2(1) + 6(2)y' = 0. Solving this equation, we find that y' = -1/6.

Therefore, the slope of the curve at the point (1, 2) is -1/6.