Question

Can someone help me? c:

Answer 1

Find k such that the line is tangent to the graph of the function.
\[f(x)=k-x^{2}\]\[y=-4x+7\]

Answer 2

First, find the derivative of f(x). You know how to do that?

Answer 3

I have but the only problem i had was what would happen to k?

Answer 4

They are two different equations. k never disappeared.

Answer 5

If this is a Calculus class, I would find the derivative first.

Answer 6

^^ I second this.

Answer 7

At the point of tangency, both equations will have the same slope. That's why we want to find the derivative...so we can figure out at what point your 2 equations will have the same slope.

Answer 8

f(x) = k - x^2
f'(x) = ______________

Answer 9

k-2x

Answer 10

That k is just a constant, so the derivative of that k is just 0...it goes away.
Sok f ' (x) = -2x

Answer 11

What is the slope of our line: y = -4x + 7 ?

Answer 12

-4

Answer 13

So, set f'(x) equal to -4 and solve for x. What do you get?

Answer 14

x=2

Answer 15

Great, that's the x-coordinate of our point of tangency. To get the y coordinate, plug x=2 back into y = -4x + 7

Answer 16

y=-1

Answer 17

yes. So now take f(x) = k - x^2 and plucg in 2 for x and -1 for y (f(x) is the same as y)
and solve for k and you're done!

Answer 18

k=3

Answer 19

That's right. Good job

Answer 20

Oh man....Thank you for your help. :) You too Chibiterasu.

Answer 21

A lot of people see that word "tangent" and don't think "oh, they have to have the same slope there" which is just the first derivative

Answer 22

No problem.