How to find the gradient of curve (i)2x^3 + 5xy +y^3 = 8 (ii) x = 2(t -2)^3 - 16 and y= 2 sin t + cos t

[Lincole Hamcarling]

 

[lev888]

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Please do what you were asked in your previous post:

"Please show us what you have tried and exactly where you are stuck.
Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem."

 

[Deleted member 4993]

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What are the co-ordinates of the points where each graph cross y-axis?

What is the "definition" of the gradient of a curve?

 

[Lincole Hamcarling]

there are no coordinate in this question ,Im stuck on both question (i) and (ii), this are the whole question , i already stuck when i see this question

 

[Deleted member 4993]

there are no coordinate in this question ,Im stuck on both question (i) and (ii), this are the whole question , i already stuck when i see this questionView attachment 28474

You are supposed to calculate those!

Hint:

When the curve crosses the y-axis, what is the x-co-ordinate of the point of intersection?

Now use the equation describing the curve and calculate the y-co-ordinate of the point of intersection?

Where is the definition of "gradient"?

 

[pka]

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The curve crosses the [imath]y[/imath]-axis where [imath]x=0[/imath].
Thus for part a) solve [imath]y^3=8[/imath].
Then using the derivative [imath]6x^2+5y+5xy^{\prime}+3y^2y^{\prime}=0[/imath]

 

[Harry_the_cat]

What are the co-ordinates of the points where each graph cross y-axis?

What is the "definition" of the gradient of a curve?

View attachment 28473

(i) Have you learnt how to do implicit differentiation?
(ii) Find dx/dt and dy/dt, then use the chain rule to find dy/dx.

In both cases, the y-int is found by letting x=0, because all points on the y-axis have an x-coord of 0.

 

[Deleted member 4993]

I think this student is not willing to show any work and expecting a "xerox-able" response, as evident from old posts.

 

[tkhunny]

Is x = f(y) or y = g(t) in the neighborhood of the points of investigation?