URGENT as level maths question help needed

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_martha
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Can anyone tell me what to do to solve the question below?

A curve has equation y=g(x) where g(x) = kx³ + 15x² -39x + c
Given that the point P(2,10) lies on the curve and that the gradient of the curve at P is -3,

a) find the values of k and c

b) hence show that the curve has no stationary points

c) write g(x) in the form (x-4)h(x) where h(x) is an expression to be found

d) hence deduce the coordinates of the points of intersection of the curve with the equation y=g(0.2x) and the coordinate axis

If someone could even help with part a that would be really helpful as then I think I can do the rest. Thanks
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gdunne42
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(Original post by _martha)
Can anyone tell me what to do to solve the question below?

A curve has equation y=g(x) where g(x) = kx³ + 15x² -39x + c
Given that the point P(2,10) lies on the curve and that the gradient of the curve at P is -3,

a) find the values of k and c

b) hence show that the curve has no stationary points

c) write g(x) in the form (x-4)h(x) where h(x) is an expression to be found

d) hence deduce the coordinates of the points of intersection of the curve with the equation y=g(0.2x) and the coordinate axis

If someone could even help with part a that would be really helpful as then I think I can do the rest. Thanks
point P is on the line - sub in the values and form an an equation
the gradient at P is -3, how do you find the gradient of a line from its equation? form another equation
Last edited by gdunne42; 1 month ago
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_martha
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(Original post by gdunne42)
point P is on the line - sub in the values and form an an equation
the gradient at P is -3, how do you find the gradient of a line from its equation? form another equation
How would I use this to find the values of c and k? I have got as far as 8k+c=28 but not sure what to do from here.
Last edited by _martha; 1 month ago
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gdunne42
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(Original post by _martha)
How would I use this to find the values of c and k?

what would you do to determine the gradient function of g(x)
(note that as c is a constant it disappears)
use the result to form another equation using (2,10) and -3
Last edited by gdunne42; 1 month ago
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_martha
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(Original post by gdunne42)
what would you do to determine the gradient function of g(x)
(note that as c is a constant it disappears)
use the result to form another equation using (2,10) and -3
Do you mean that you would differentiate the original equation for g(x) or assume that the second differential is g''(x)=-3x+16 based on the information given about point P?
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gdunne42
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(Original post by _martha)
Do you mean that you would differentiate the original equation for g(x) or assume that the second differential is g''(x)=-3x+16 based on the information given about point P?
I would differentiate g(x) to form another equation where you can substitute x=2 and g'(x)=-3 to solve k and hence solve c from your first result
Last edited by gdunne42; 1 month ago
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_martha
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(Original post by gdunne42)
I would differentiate g(x) to form another equation where you can substitute x=2 and g'(x)=-3 to solve k and hence solve c from your first result
Thank you so much I've got it now!
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gdunne42
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(Original post by _martha)
Thank you so much I've got it now!
Great, questions like this where you're given lots of info and can form and solve equations simultaneously are common in A level exams. Especially with functions and their derivates and also with the factor theorem/remainder theorem.
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