Question

Find the equation of the tangent line to f(x) = 9 − x^2 through the point (5, 0) that touches f (x) at a point below the x-axis.

Answer 1

first you need to find the slope at this point

Answer 2

-2x ?

Answer 3

that is the function of all the slopes wrt to x

Answer 4

f(x) is telling you all the heights at every x
f'(x) is teelling you all the slopes at every x
now at what x do we need to know our f'(x)

Answer 5

the point where it touches f(x) which is below the x axis?

Answer 6

take a look at your point

Answer 7

(5, 0)

Answer 8

whats the x value of the point

Answer 9

5

Answer 10

right so we need to know f'(5) = ?

Answer 11

But that point doesn't even lie on the curve...

Answer 12

we just want the slope there at x=5

Answer 13

so that would be -2(5) = -10, right?

Answer 14

oh wait 5,0 isnt on this curve really?

Answer 15

u are right lol xD

Answer 16

Yeah cause try plugging it in the function

Answer 17

XD

Answer 18

I think we should first find a point that apparently lies somewhere under the x-axis

Answer 19

k lets graph and see what exactly is going on here