Question

In Exercises 35 through 42, the slope $f'(x)$ at each point $(x, y)$ on a curve $y = f(x)$ is given along with a particular point $(a, b)$ on the curve. Use this information to find $f(x)$. 35. $f'(x) = 4x + 1$; $(1, 2)$ 36. $f'(x) = 3 - 2x$; $(0, -1)$ 37. $f'(x) = -x(x + 1)$; $(-1, 5)$ 38. $f'(x) = 3x^2 + 6x - 2$; $(0, 6)$ 39. $f'(x) = x^3 - frac{2}{x^2} + 2$; $(1, 3)$ 40. $f'(x) = x^{-1/2} + x$; $(1, 2)$ 41. $f'(x) = e^{-x} + x^2$; $(0, 4)$ 42. $f'(x) = frac{3}{x} - 4$; $(1, 0)$

          In Exercises 35 through 42, the slope $f'(x)$ at each point $(x, y)$ on a curve $y = f(x)$ is given along with a particular point $(a, b)$ on the curve. Use this information to find $f(x)$. 
35. $f'(x) = 4x + 1$; $(1, 2)$
36. $f'(x) = 3 - 2x$; $(0, -1)$
37. $f'(x) = -x(x + 1)$; $(-1, 5)$
38. $f'(x) = 3x^2 + 6x - 2$; $(0, 6)$
39. $f'(x) = x^3 - frac{2}{x^2} + 2$; $(1, 3)$
40. $f'(x) = x^{-1/2} + x$; $(1, 2)$
41. $f'(x) = e^{-x} + x^2$; $(0, 4)$
42. $f'(x) = frac{3}{x} - 4$; $(1, 0)$

$In Exercises 35 through 42, the slope f'(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find f(x). 35. f'(x) = 4x + 1; (1, 2) 36. f'(x) = 3 - 2x; (0, -1) 37. f'(x) = -x(x + 1); (-1, 5) 38. f'(x) = 3x^2 + 6x - 2; (0, 6) 39. f'(x) = x^3 - frac2x^2 + 2; (1, 3) 40. f'(x) = x^-1/2 + x; (1, 2) 41. f'(x) = e^-x + x^2; (0, 4) 42. f'(x) = frac3x - 4; (1, 0)$

Added by Lori B.

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