Question

Calculus
Topic: Tangent Lines

Answer 1

well you're given two points,
so you can write the equation for line ?

Answer 2

equation of line passing thru (-1, 4) and (3, 6) is ?

Answer 3

m=y2-y1/x2-x1
m=6-4/3--1
m=2/4
m=1/2

y=1/2x+b
6=1.5+b
6-1.5=b
4.5=b

y=0.5x+4.5

Answer 4

m = 1/2 is correct

Answer 5

b is not correct, check again

Answer 6

hey no, you're right sorry :|

Answer 7

y=1/2x+b
4=-0.5+b
4.5=b

Answer 8

Oh yay

Answer 9

i messed up my calculation lol

Answer 10

It's okay i make way more mistakes :p

Answer 11

ok so equation of tangent at \(x = -1\) for the function \(y = h(x)\) is

\(y = 0.5x + 4.5\)

Answer 12

so, the given point (-1, 4) will lie on both \(tangent\) and \(y=h(x)\) right ?

Answer 13

so,
\(h(-1) = ?\)

Answer 14

4

Answer 15

Perfect !

Answer 16

wat about \(h'(-1)\) ?

Answer 17

:)

Answer 18

recall the definition of \(derivative \) at a point :-

\(derivative\) at -1, \(h'(-1)\) gives the slope of \(tangent\) line at x = -1

Answer 19

\[h'(-1)= \lim_{x \rightarrow -1}\frac{ h(x)+h(-1) }{ x-a }\]

Answer 20

noo, you already worked the slope of tangent line