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Jayati Sindhu Grade: 12
        y=f(x) is a parabola, having its axis parallel to y axis. If the line y=x touches this parabola at x=1, then find the relation between f"(1) and f'(0).
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Jayati


we can write general equation of parabola whose vertics is parallel to y axis


(y-b) = c(x-a)2


y = c(x-a)2 + b


so f(x) = c(x-a)2 + b


now y=x is tangent to parabola


f'(x) = 2c(x-a)


f''(x) = 2c


f'(1)=1 = 2c(1-a) 


 1 = 2c -2ca   ............1


f'(0) = -2ca


f''(1) =2c


put these value in equation 1


 1 = f''(1) +f'(0)


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Badiuddin



7 years ago
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