Question

Give an example of a polynomial function that meets the above criteria

Answer 1

Answer:

F(x) = -5x - 8

Explanation:

Let's try with the polynomial function

f(x) = -5x - 8

We can calculate f(8) replacing x by 8, so:

f(8) = -5(8) - 8

f(8) = -40 - 8

f(8) = -48

Additionally, f'(x) will be equal to:

f'(x) = -5

And -5 is distinct from 0.

Finally, if f'(x) = -5, f''(x) is the derivative of a constant, so:

f''(x) = 0 for all x

Therefore, an function that satisfies all the conditions is:

F(x) = -5x - 8