hi-everyone-what-is-the-definition-of-the-tangent-straight-line-to-the-curve-without-relying-to-the-derivitve-because-the-derivative-is-the-slope-and-thanx-for-all-

Question Number 89698 by M±th+et£s last updated on 18/Apr/20

h i e v e r y o n e

w h a t i s t h e d e f i n i t i o n o f t h e t a n g e n t

s t r a i g h t l i n e t o t h e c u r v e w i t h o u t r e l y i n g

t o t h e d e r i v i t v e

b e c a u s e t h e d e r i v a t i v e i s t h e s l o p e

a n d t h a n x f o r a l l

Commented by mr W last updated on 18/Apr/20

t h e d e r i v a t i v e i s t h e s l o p e, t h i s i s

c o r r e c t . b u t w h o s e s l o p e ? i t i s t h e

s l o p e o f t h e t a n g e n t l i n e! r e a d t h e

d e f i n i t i o n o f d e r i v a t i v e i n y o u r b o o k,

{y o u}^{'} l l s e e .

Commented by M±th+et£s last updated on 18/Apr/20

t h a t i s r i g h t t h a n k y o u b u t i w a n t t h e t a n g e n t l i n e

d e f i n i t i o n n o t t h e s l o p e o f t h e t a n g e n t

l i n e

Commented by Kunal12588 last updated on 18/Apr/20

i f y o u k n o w t h e s l o p e o f t a n g e n t a n d a p o i n t

f r o m w h e r e t h e t a n g e n t i s p a s s i n g . w e c a n f i n d

{e q}^{n} o f t a n g e n t

Commented by M±th+et£s last updated on 19/Apr/20

t h a n k y o u s i r i k n o w h o w c a n i f i n d

t h e {e q}^{n} b u t i w a s a s k i n g a b o u t t h e t a n g e n t

l i n e d e f i n t i o n

Answered by MJS last updated on 18/Apr/20

the tangent line to a curve in a given point

is defined as the limit of secants .

let y = f (x) and P = (\begin{matrix} p \\ f (p) \end{matrix})

further let O = (\begin{matrix} p - h \\ f (p - h) \end{matrix}) and Q = (\begin{matrix} p + h \\ f (p + h) \end{matrix})

then the lines l_{h} : X = O + λ \overset{⇀}{O Q} or

{\begin{cases} x = p - h + 2 λ h \\ y = f (p - h) + λ (f (p + h) - f (p - h)) \end{cases} with

h > 0 and λ \in R are secants to the curve

y = f (x) .

let h \to 0 \Rightarrow l_{0} is the tangent in P

if the curve is concave or convex in P, l_{0}

touches the curve in P . if the curve has a

turning point (= inflection) in P, l_{0}

intersects the curve in P

Commented by M±th+et£s last updated on 18/Apr/20

i {d o n}^{'} t k n o w h o w c a n i t h a n k f o r t h i s

g o d b l e s s y o u s i r

Commented by MJS last updated on 18/Apr/20

{you}^{'} re welcome

“ i t i s m o r e b l e s s e d t o g i v e t h a n i t i s t o {r e c i e v e}^{″}

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