Mathematics

Mathematics

Problem

### Passage IV (Q. Nos. 55 to 57)

f(x) = \int_{0}^{x} (4t^4 - at^3) dt

and

g(x)

is quadratic satisfying

g(0) + 6 = g'(0) - c = g''(c) + 2b = 0

.

y = h(x)

and

y = g(x)

intersect in 4 distinct points with abscissae

x_i

;

i = 1, 2, 3, 4

such that

\sum_{i} \frac{1}{x_i} = 8

,

a, b, c \in \mathbb{R}^+

and

h(x) = f'(x)

. '

a

' is equal to a. 6 b. 8 c. 20 d. 12

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