A few days ago
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
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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