Question

For what values of a and b is the line 2x+y=b tangent to the parabola y = ax^2 when x = 2?

Answer 1

Have you found y'?

Answer 2

of which ONE

Answer 3

Find y' and put 2x+y=b into this form: y=mx+c to find m
Then set y'=m

Answer 4

like y' = 2ax? that one? i start there?

Answer 5

ok now set y'=the slope of the tangent line

Answer 6

uh you mean like 2x + y = b ==> y = -2x+b .. ?

Answer 7

and also we want to know what a is when x=2
so we have
2a(2)=the slope of the tangent line

Answer 8

oy

Answer 9

y=-2x+b
so the slope of tangent line is -2 right?

Answer 10

\[2a(2)=-2\]
solve for a! :)

Answer 11

ah

Answer 12

\[a=-\frac{1}{2}\]
we also need to find b though!

Answer 13

when x=2, what is f(2)?

Answer 14

i will let you tell me

Answer 15

f(x)=ax^2
we found a
what is f(2)?

Answer 16

The reason we need this is so we can know a point on the tangent line so we can solve for b

Answer 17

2x+y=b
2(2)+f(2)=b
4+f(2)=b

so once you find f(2) you will be able to find b

Answer 18

Right
We could say that with out the bad language part though please

Answer 19

without*