The graph of a function of degree 3 has a tangent parallel to the first angle bisector at the point P(1;4) and a tangent parallel to the x-axis at Q(0;2).?

kimialalalandBykimialalaland

Hi, I've been trying to solve this problem for two days, but I can't seem to find a solution and my solution is wrong every time I try. Can someone please help?

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evtldocha
evtldocha
1 year ago

Approach:

(The 2nd discharge is not required here)

The conditions are:

Note:

  • The angle halving has the pitch 1 and thus also each straight line parallel thereto has the pitch 1
  • “parallel to the x-axis” means “state equal to 0”

The associated equation system is:

(1)   a +   b +   c +   d = 4
(2) 3·a + 2·b +   c       = 1
(3) 0·a + 0·b +   c       = 0
(4) 0·a + 0·b + 0·c +   d = 2

The solution of the equation system is

and the function is:

Sketch:
1
kimialalaland
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kimialalaland
1 year ago
Reply to  evtldocha

THANKS

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Rhenane
Rhenane
1 year ago

It would have been nice, of course, to show your conditions and your way of calculating…

here the required conditions (for function 3. Grades are the 4), possibly there is the error:
(I) point P(1|4) => f(1)=4
(II) parallel to the angle halving (=g(x)=x), i.e. the same gradient as this => f'(1)=1
(III) point Q(0|2) => f(0)=2
(IV) parallel to the x axis, means gradient 0, i.e.: f'(0)=0

1