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  • Try this! Let a curve y=f(x) passes through (1,2) . If tangent drawn at (1,2 ) to y= f(x) has slope 3/4 then f'(1) equals

Let a curve y=f(x) passes through (1,2) . If tangent drawn at (1,2 ) to y= f(x) has slope 3/4 then f'(1) equals 

  • Option 1)

    3/4

  • Option 2)

    4/3

  • Option 3)

    -4/3

  • Option 4)

    -3/4

 

Answers (1)

best_answer

As we have learned

Geometrical interpretation of Derivative -

Let P be any point (x, y)  on the curve  y = f(x) and Q is a point in the neighbourhood of  P  on either side of  P. such that the co-ordinate of the point Q are 

(x+\delta x, y+\delta y)  satisfying the curve y = f(x)

\therefore \:M_{T}=slope\:of\:tangent

=\lim_{\delta x\rightarrow \circ }\:\:\frac{(y+\delta y)-y}{(x+\delta x)-x}=\lim_{\delta x\rightarrow \circ }\:\:\frac{\delta y}{\delta x}


\therefore \:\:M_{T}=(\frac{dy}{dx})\:\:at \;\:(x,\:y)

- wherein


Where (x, y)  on the curve and  MT  is tangent at (x, y).

 

 f'(1) is derivative of f(x) at point with x- coordinate 1 . so  f'(1) is slope of tangent at point with x-coordinate 1 ,  which is already given to be 3/4

f'(1)= 3/4 

 

 

 

 


Option 1)

3/4

Option 2)

4/3

Option 3)

-4/3

Option 4)

-3/4

Posted by

Himanshu

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