Is there a function f(x) satisfying all of the following conditions:

Question

Is there a function f(x) satisfying all of the following conditions:

i. f(x) is a continuous function on the interval [−20, 0]

ii. f(x) is differentiable on the interval (−20, 0) and the derivative of f(x) is 0 on the interval (−20, 0), i.e. f'(x) = 0 on (−20, 0)

iii. f(−5) = 6

Justify your answer.

Answer 1

The derivative is zero which means the function must be constant...

f(-5)=6 ---> y = f(x) = 6