Find f. f ''(𝜃) = sin(𝜃) + cos(𝜃), f(0) = 4, f '(0) = 2

Answer 1

f"(x) = sinT + cosT

f'(x) = -cosT + sinT + C

f'(x) = -cos(0) + sin(0) + C = 2

-1 + 0 + C = 2

C = 3

f'(x) = -cosT + sinT + 3

f(x) = -sinT -cosT + 3x + D

f(0) = 4 = -sin(0) - cos(0) +3(0) + D

4 = 0 -1 + D

D = 5

f(x) = -sinT -cosT + 3x + 5