If the limit definition of a derivative can be used to find f'(x), then what is the purpose of using other rules to find f'(x)? . . . Choose the correct answer below. O A. The other rules for derivatives are easier to use and may take less time than the limit definition. O B. The limit definition cannot be used to find the derivative of a function of the form f(x) = nx. O C. The limit definition cannot be used to find the derivative of a function of the form f(x) = -, n # 0. O D. The other rules for derivatives can be used to check the answer found by using the limit definition.Let F(x) = f(x) + g(x), where the graphs of f and g are shown in the gure to the right. Find F'(1). Next question 10 om>mm F'(1)= Let H(x) = 4f(x) + 2g(x), where the graphs of f and g are shown in the figure to the right. Find H'(2). Next question Ay=g(X ) X 8 10 H' (2) =\f When observations begin at t= 0, a cell culture has 1600 cells and continues to grow according to the function p(t) = 1600 e t, where p is the number of cells and t is measured in days. 3. Compute p'(t). What units are associated with the derivative and what does it measure? b. On the interval [0,9] when is the growth rate p' (t) the least? When is it the greatest? a. p'(t) = (Type an exact answer in terms of e.) a. Find an equation of the tangent line at x = a. b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. y=ex;a=ln11 a. At x = a, an equation of the tangent line is y = D. Let f(x) = 2x2 -12x + 3. a. Find the values of x for which the slope of the curve y = f(x) is 0. b. Find the values of x for which the slope of the curve y = f(x) is - 4. a. The slope of the curve is 0 at x = D. (Simplify your answer. Use a comma to separate answers as needed.) \fLet F =f+ 9, where the graphs of f and g are shown in the gure to the right. Find the following derivative. Next question Av Q ' Q F'(1) F'(1)= The following limit represents f'(a) for some function f and some value of a. Jmm 4% lim h>0 h a. Find a function fand a number a. b. Determine the value of the limit by nding f'(a). E) a. f(x) = E (Type an expression using x as the variable. Type an exact answer, using radicals as needed.) a=D (Type an integer or a decimal.) Use a calculator to approximate the following limit. e 9x 1 lim X X-0 9X e - 1 lim (Type an integer or a decimal.) X X- 0Use a calculator to approximate the following limit. lim x* X-+0* lim x* = (Type an integer or a decimal.) X-0 Suppose p(t) = - 0.23t3 + 111t2 + 7637t + 70,000 is the population of a city t years after 1994. a. Determine the average growth rate from 1994 to 2004. b- What was the growth rate for this city in 1996 (when t= 2)? a. The average growth rate from 1994 to 2004 is D people! year. (Type an integer or a decimal.) The following limit represents f\"(a) for some function f and some value a. a. Find the simplest function fand a number a. b. Determine the value of the limit by nding f'(a). 170 x 1 x1 a. Select the correct choice below and ll in the answer box within your choice. (Type an integer or a decimal.) O A. f(x)=x169;a=|:| O B. f(x)=x171;a=|:| O C. f(x)=x170;a=|:|