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  • Can someone explain Let f(x) is a continous in [a, b] and differenciblefunction in (a, b) then the number of tangents that can drawn on f(x) within ont parallel to chord joining (a, f(a)) and (b, f(b)) is

Let f(x) is a continous in [a, b] and differencible function in (a, b) then the number of tangents that can drawn on f(x) within ont parallel to chord joining (a, f(a)) and (b, f(b)) is

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    at least one

 

Answers (1)

best_answer

As we have learned

Geometrical interpretation of Lagrange's theorem -

Let  A, B  be the points on the curve  y = f(x)  at  x = a  and   x = b  so that  A [a, f(a)],  and  B [b, f(b)]

\therefore \:\:slope\:of\:chord\:AB

=\frac{f(b)-f(a)}{b-a}

So slope of the chord  AB = f'(c)  the slope of the tangent to the curve at  x = c.

- wherein

 

 \because f(x) satisfies condition of L.M.V.T , so there exists atleast one 'c' such that f'(c) = \frac{f(b)-f(a)}{b-a}  i.e at least one 'c' where tangent is parrallel to chord

 

 

 

 

 


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

at least one

Posted by

Himanshu

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