graphing help

\fQuestion 11: (3 points) Given f (4) = 5, f'(4) = 7, g(4) = -1, and g' (4) = 9, find the values of the following. (a) (fg)' (4) = _ (b) Question 12: (6 points) Find the equation of the tangent line to the graph of the function f (x) = (x2 + 10 ) (x - 3) at the point (1, -22). y Show your work and explain, in your own words, how you arrived at your answer.\fQuestion 6: [5 points) -5 = 1 For what value of c is the function / () = 2 continuous at = = -57 25 (=45) (2 6) otherwise Show your work and explain, In your own words, how you arrived at your answer. Question 7: [S pointe) Use the Intermediate Value Theorem to show that the given function has a zero in the interval (0, 2]. f (z) =12 +21-7 f (=) on the interval D, 2). f(0) = f (2) = By the Intermediate Value Theorem, there is a value c in [0, 2] such that / (c) = 0, since f (0) 0 and f (2) 0.Question 8: [5 pointe) The following le Moblue" explanation for a solution to this question. You can use this and other online references as a guide, but your explanation should be In your own words. The derivative of a function of f at I is given by f' (z) = lim _ f(Ith)-f(z) h provided the limit exists. Use the definition of the derivative to find the derivative of f (2) = 72- + 2: + 9 Enter the fully simplified expression for f(x + /) - f (x). Do not factor. Make sure there is a space between variables. f ( z th) - f (z) =_ f (z) = Show your work and explain, In your own words, how you arrived at your answers. Question 9: [2 points) Find the derivative of f (2) =7213 -15 +8. f (I) = Question 10: (2 points] Find the derivative of f (w) = wd + 7 Enclose numerators and denominators in parentheses. For example (a - b)/ (1 + n)- f' (10) =