Question

Find f.
f"(x) = 24x² + 2x + 10, f(1) = 5, f'(1) = -3

Answer 1

f''(x) = 24x² + 2x + 10

f'(x) = 8x³ + x² + 10x + A

f'(1) = 8(1³) + 1² + 10(1) + A

-3 = 8 + 1 + 10 + A

19 + A = -3

A = -22

f'(x) = 8x³ + x² + 10x - 22

f(x) = 2x⁴ + (1/3)x³ + 5x² - 22x + B

f(1) = 2(1⁴) + (1/3)(1³) + 5(1²) - 22(1) + B

5 = 2 + 1/3 + 5 - 22 + B

15/3 = -44/3 + B

B = 59/3

f(x) = 2x⁴ + (1/3)x³ + 5x² - 22x + (59/3)