Answer:
We are given:
f(1) = 8
f'(1) = 3
f''(1) = 4
Using these conditions, we can write three equations:
f(1) = a(1)^2 + b(1) + c = 8
f'(1) = 2a(1) + b = 3
f''(1) = 2a = 4
Simplifying the last equation, we get:
2a = 4
a = 2
Substituting this value of a in the second equation, we get:
2(1) + b = 3
b = 1
Substituting the values of a and b in the first equation, we get:
2(1)^2 + 1(1) + c = 8
c = 5
Therefore, the values of a, b, and c are:
a = 2
b = 1
c = 5
Hence, f(x) = 2x^2 + x + 5.