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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)

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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```
7 years ago
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