plz. help,,,,,,ASAP?

CALCULUS

1.) Make the parabola y=ax^2+bx=c pass through (2,1) and be tangent to y=2x+4 at (1,6)

2.) Make cubic y=ax^3+bx^2+cx+d be tangent to y=12x+13 at (-1,1) and have a horizontal tangent at the point (1,5)

3.) Make the cubic y=ax^3+bx^2+cx+d pass through the points (0,6)(1,-2) and be tnagent to 3x-y=6 at (2,0)

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

1) Since the parabola passes through (2,1), we have the equation:

1=4a+2b+c.

Since the parabola is tangent to the line y=2x+4 at (1,6), the parabola passes through (1,6):

6 = a + b + c

and the parabola’s slope

y’=2ax + b

at x=1 must be equal to the slope of the line:

2a + b = 2.

Solving three simultaneous equations

4a + 2b + c = 1

a + b + c = 6

2a + b = 2

we find

a = -7

b = 16

c = -3

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