Let g(x) be a continuous function and let g(") (x) be the n-th derivative of g(x). Find an example of g(x) such that gm) (x)| < 1 for all n and for all x E R.

Suppose F(t) has the derivative f(t) shown below, and F(0) = 6. Find values for F(2) and F(7) 3- 2 1 2 -1 -2 -3 F(2) = F(7) = + 5

Prove that the function ax+b f(x)= cx+d is constant (takes the same value for every x such that cx+d #0) if and only if (Hint: Find the derivative of f(x).) a с |=0.