Suppose that has a positive derivative for all values of x and that (1) = 0. Which of the following statements must be true

Suppose that ƒ has a positive derivative for all values of x and that ƒ(1) = 0. Which of the following statements must be true of the function

Give reasons for your answers.

a. g is a differentiable function of x.

b. g is a continuous function of x.

c. The graph of g has a horizontal tangent at x = 1.

d. g has a local maximum at x = 1.

e. g has a local minimum at x = 1.

f. The graph of g has an inflection point at x = 1.

g. The graph of dg/dx crosses the x-axis at x = 1.

g(x) = Xu 0 f(t) dt?