Question

find a function f that satisfies the condition

f''(x) = 2, f'(2) = 5 , f(2) = 10

this is antiderivatives and indefinite integrals (ie. applications of it)

Answer 1

f'(x) = 2x +C
f'(2) = 5 ==> 2(2) +C = 5 ==> C = 1
f'(x) = 2x + 1
f(x) = x^2 + x + C
f(2)=10 ==> 2^2 +2 +C = 10 ==> C=4
f(x) = x^2 + x +4

Answer 2

thank you! i understand