jee-main 2024 Q76

jee-main · India · session1_30jan_shift2 Exponential Functions Parameter Determination from Conditions
Let $f: R \rightarrow R$ be defined $f(x) = ae^{2x} + be^x + cx$. If $f(0) = -1$, $f'(\log_e 2) = 21$ and $\int_0^{\log 4} (f(x) - cx)\, dx = \frac{39}{2}$, then the value of $|a + b + c|$ equals:
(1) 16
(2) 10
(3) 12
(4) 8
Let $f: R \rightarrow R$ be defined $f(x) = ae^{2x} + be^x + cx$. If $f(0) = -1$, $f'(\log_e 2) = 21$ and $\int_0^{\log 4} (f(x) - cx)\, dx = \frac{39}{2}$, then the value of $|a + b + c|$ equals:\\
(1) 16\\
(2) 10\\
(3) 12\\
(4) 8