Question

Consider the parabola y = 4x − x2.
(a) Find the slope of the tangent line to the parabola at the point (1, 3).

Answer 1

do u know derivatives?

Answer 2

i'm just getting into them

Answer 3

i know what they are

Answer 4

i got it

Answer 5

just plug in 1 and get 2

Answer 6

(b) Find an equation of the tangent line in part (a).

Answer 7

ok u have
\[ \large f(x)=4x-x^2 \]
find \(f'(x)\)

Answer 8

then the tangent line at (1,3) will be
\[ \large y-3=f'(1)\cdot(x-1) \]

Answer 9

how did you get there?

Answer 10

to define a line u need either two points or one point and the slope.

in this case u have the point (1,3) and the slope of the tangent which is the derivative.

Answer 11

ok

Answer 12

did u get \(f'(1)=\)

Answer 13

no

Answer 14

is it 0?

Answer 15

\[ \large f(x)=4x-x^2 \]
then
\[ \large f'(x)=4-2x \]
so
\[ \large f'(1)=4-2\cdot1=2 \]

Answer 16

ohh

Answer 17

this is the slope of the tangent line

Answer 18

ok