Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

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…

Help find a function f so that f ‘(x) = 3x2+ 2x+5 and f (1) = 10

What is the domain of this function