Let fand g be inverse functions that are differentiable for all x. If f(3) = -2 and g' (-2) = -4, which of the following statements must be false? I. f'(0) = 1 II. f'(3) II. f'(5) 4 - A | I only B Il only III only D I and III only

Letf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3. Using the above information, compute h' (-6) where h(x) = (f(x))² g(x). h'(- 6) = Number

Let x + 1 f(x) * + 10 f'(- 7) :

A company's revenue from car sales, C (in thousands of dollars), is a function of advertising expenditure, a, in thousands of dollars, so C = f(a). (a) What does the company hope is true about the sign of f'? O The company hopes f'(a) is always positive. O The company hopes f'(a) is always negative. The company hopes f'(a) equals zero. The company has no sign preference. O The company hopes f'(a) is sometimes negative and sometimes positive. (b) What does the statement f'(100) = 2 mean in practical terms? O f'(100) means that if the advertising budget is $2,000, the company's revenue is $100. O f'(100) means that if the advertising budget is $100,000 the company's revenue is $2. O f'(100) means that if the advertising budget is $100,000 each extra dollar spent on advertising will bring in about $2 worth of sales. O f'(100) means that the company must sell 2 cars in order to pay for $100,000 worth of advertising. O f'(100) means that if the advertising budget is $2,000, each extra…