Question

determine b and c, so that the graph of the function x^2 + bx + x touches the straight line y=x in point (1,1)

Answer 1

Correction :it's x^2 + bx + c

Answer 2

Does the line y=x have to be tangent to the curve, or is the only stipulation that (1,1) is on the curve?

Answer 3

y=x has a constant slope of 1, so what you are looing for is the equation of a parabola where y=x is tangent to that parabola at the given point.

Taking the first derivative of y = x^2 + bx + c we have:

y' = 2x + b

and we need that first derivative to be "1" at point (1, 1)

1 = 2(1) + b -> so b = -1

Back to the parabola, we have so far: y = x^2 - x + c

and we need y to be 1 when x = 1, so:

1 = (1)^2 - (1) + c so, c = 1

So our parabola is:

y = x^2 - x + 1

Answer 4

i had to take the derivative! ofcourse!

Answer 5

that's where i was stuck

Answer 6

That's ok, you're unstuck now!

Answer 7

jep, thanks!

Answer 8

uw, very much! Good luck to you in all of your studies and thx for the recognition! @Rowa

Answer 9

np

Answer 10

Here's something you m1ght like, @Rowa