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Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3?
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Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3?
Gradient of the Curve at Point (3,2)
- First, we need to find the gradient of the curve y-xy 2px 3qy=0 at the point (3,2).
- To do this, we will differentiate the given equation implicitly with respect to x.
Implicit Differentiation
- Differentiating y-xy 2px 3qy=0 with respect to x, we get:
dy/dx - y - x(dy/dx) - 2p + 3q(dy/dx) = 0
Substitute Point (3,2)
- Now, substitute the point (3,2) into the equation we obtained:
dy/dx - 2 - 3(dy/dx) - 2p + 6q = 0
Solve for dy/dx
- Rearrange the equation and solve for dy/dx:
dy/dx - 3(dy/dx) = 2 + 2p - 6q
- Simplifying further, we get:
-2(dy/dx) = 2 + 2p - 6q
dy/dx = (2 + 2p - 6q)/(-2)
dy/dx = -1 - p + 3q
Substitute Point (3,2)
- Now, substitute the values x=3 and y=2 into dy/dx:
dy/dx = -1 - p + 3q
dy/dx = -1 - 4 + 6
dy/dx = 1
Conclusion
- Therefore, the gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is 1, not -2/3 as stated.
- First, we need to find the gradient of the curve y-xy 2px 3qy=0 at the point (3,2).
- To do this, we will differentiate the given equation implicitly with respect to x.
Implicit Differentiation
- Differentiating y-xy 2px 3qy=0 with respect to x, we get:
dy/dx - y - x(dy/dx) - 2p + 3q(dy/dx) = 0
Substitute Point (3,2)
- Now, substitute the point (3,2) into the equation we obtained:
dy/dx - 2 - 3(dy/dx) - 2p + 6q = 0
Solve for dy/dx
- Rearrange the equation and solve for dy/dx:
dy/dx - 3(dy/dx) = 2 + 2p - 6q
- Simplifying further, we get:
-2(dy/dx) = 2 + 2p - 6q
dy/dx = (2 + 2p - 6q)/(-2)
dy/dx = -1 - p + 3q
Substitute Point (3,2)
- Now, substitute the values x=3 and y=2 into dy/dx:
dy/dx = -1 - p + 3q
dy/dx = -1 - 4 + 6
dy/dx = 1
Conclusion
- Therefore, the gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is 1, not -2/3 as stated.
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Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3?
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Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3?.
Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Gradient of the curve y-xy 2px 3qy=0 at the point (3,2) is -2/3?.
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