Given the relationx^2+y^2 =25. Determine the slope of the tangent at the point (-3,4).m = Answer
Question
Given the relationx^2+y^2 =25. Determine the slope of the tangent at the point (-3,4).m = Answer
Solution
To find the slope of the tangent line to the curve at a given point, we first need to find the derivative of the function. The given equation is in implicit form, so we'll need to use implicit differentiation.
The equation is x^2 + y^2 = 25.
Differentiate both sides with respect to x:
2x + 2y*(dy/dx) = 0.
Solve for dy/dx (the derivative of y with respect to x, which gives us the slope of the tangent line):
dy/dx = -x/y.
We're asked to find the slope at the point (-3,4), so substitute x = -3 and y = 4 into the equation:
m = dy/dx = -(-3)/4 = 3/4.
So, the slope of the tangent line at the point (-3,4) is 3/4.
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