Question 1026683
f"(x) = {{{3x^2-5sinx+2e^x}}}

==> f'(x) = {{{x^3+5cosx+2e^x+c}}} for some constant c.

f'(0) = 10 ==> {{{10 = 0^3+5cos0+2e^0+c}}} ==> c = 3.

==> f'(x) = {{{x^3+5cosx+2e^x+3}}}

==> {{{f(x) = x^4/4 + 5sinx + 2e^x + 3x + k}}} for some constant k.
f(0) = 0 ==> {{{f(0) = 0^4/4 + 5sin0 + 2e^0 + 3*0 + k = 0}}} ==> k = -2.

{{{highlight(f(x) = x^4/4 + 5sinx + 2e^x + 3x - 2)}}}