Initial Value Problems

Solve the following initial value problems.

  a) \( f'(x) = 1+3x^2,\quad f(-1) = 2 \)    solution

  b) \( f'(x) = 2 x - \frac{1}{x}, \quad f(1) = 5 \)   solution

  c) \( f'(x) = \frac{1}{\sqrt x}, \quad f(4) = 2 \)    solution

 d) \( f'(x) = 2e^{x}-10x, \quad f(0) = 11 \)  solution