Using Mean Value Theorem, find a point on the curve y=(x-3)^2, where the tangent is parallel to the chord joining - Maths - Continuity and Differentiability

Question

Using Mean Value Theorem, find a point on the curve y=(x-3)^2,
where the tangent is parallel to the chord joining the points (3,0)
and (4,1)

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

fx=x-32fx is polynomial function
 So, it is continous in 3,5
f'x=2x-3It is also derivable
f3=3-32=0f4=4-32=1f'c=2c-3Applying MVT2c-3=f4-f34-32c-3=1-0c-3=12c=3+12c=72For x=72 , tangent to curve is parallel to chord joining 3,0 and 4,1
Put x=72 in curvef72=72-32=122=14Point is 72,14 
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Using Mean Value Theorem, find a point on the curve y=(x-3)^2, where the tangent is parallel to the chord joining the points (3,0) and (4,1).