7. If f is a differentiable function and f(0) = -1 and f(4) = 3, then which of the following must be true? I. There exists a c in (0,4] where f(c) = 0.
II. There exists a c in (0,4] where f'(c) = 0.
III. There exists a c in (0,4] where f'(c) = 1.
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

whatare you sayig

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places