Another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind..

another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind...

quadratics having a common tangent

x^2 + ax + b and y = cx -x^2 have a common tangent line at the point (1,0). Find a, b, and c.

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problem 2

find dy / dt

y= 4 sin ( sqrt (1+ sqrt (x) )

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find value of the derivative of (f o g) @ the given value of x. f(u) = 2u/u^2 + 1 , u = g(x) = 1/x^2 - 1 , x = -1

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Another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind...?

f(x) = x^2 + ax + b , g(x) = cx - x^2 have a common tangent line at the point (1,0). This means

f'(1) = g'(1)

Let's solve for f'(x) and g'(x).

f'(x) = 2x + a. g'(x) = c - 2x

f'(1) = 2(1) + a = 2 + a

g'(1) = c - 2(1) = c - 2

Since f'(1) = g'(1), then

2 + a = c - 2

It also follows that they both go through the point (1,0), so

f(1) = 0 = 1^2 + a(1) + b = 1 + a + b

1 + a + b = 0

g(1) = 0 = c(1) - 1^2 = c - 1 = 0

c - 1 = 0

Three equations, three unknowns:

2 + a = c - 2

1 + a + b = 0

c - 1 = 0

The third equation implies c = 1. This means we can get "a" from the first equation.

2 + a = 1 - 2

2 + a = -1

a = -3

And we can get b from the second equation, given a = -3 and

c = 1.

1 + (-3) + b = 0

-2 + b = 0

b = 2

a = -3, b = 2, c = 1

Another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind...?

This will take me about ten min. But why should I do your work and you get quiz credit. That is pretty lazy isn't it?

Another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind...?

do your own work! how else are you gonna learn?

Another problem... it counts as a quiz... if you can't get it within 3-4 hours then nevermind...?

Solving 1 for U

The point (1,0) verifies every eq.

So 1+a+b=0 --%26gt; a+b= -1

%26amp; c-1 = 0 --%26gt; c=1

The slope of the tangent is the samt at the point (1,0) for the two curves

2x + a = c -2x at(1,0)

i.e 2+a = c - 2 = -1

So a = -3 , b =2 , c=1