Question

Determine the function f(x) satisfying the given conditions.

f''(x) = 0
f'(5) = 1
f(4) = -2

Answer 1

f''(x) means function is of grade 1
f(x) = ax + b

f'(x) = a
f'(5) = 1 ⇒ a = 1

f(4) = -2
f(4) = 1×4 + b
-2 = 4 + b
b = -6

f(x) = x - 6