Suppose that f(0) = −5 and f '(x) ≤ 7 for all values of x. how large can f(5) possibly be?

f(5) cannot exceed 30.

Step-by-step explanation:

f is differentiable in all R, so we can apply the Mean Value Theorem on the interval [0,5], since f is continuous on [0,5] and differentiable on (0,5).

By the MVT, there exists some number c∈(0,5) such that . Substituting the value of f(0), this last equation is equivalent to . But f'(x)≤7 for all values of x, in particular for x=c, so applying this bound we obtain that . Then , so substracting 5 from both sides we conclude that .

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

5104.38 inches

step-by-step explanation: