Please solve the following questions

13. Let f be a twice differentiable function with f(1) =-1, f'(1) = 2, and f'(1) =0. Let g be a function whose derivative is given by g'(x) = x- [2f(x) + f'(x)] for all x. (a) Write an equation for the line tangent to the graph of f at x =1. (b) Does the graph of f have a point of inflection when x = 1? Explain (c) Given that g(1) = 3, write an equation for the line tangent to the graph of g at x =1. (d) Show that g'(x) = 4x f(x)+2x(x+1)f(x)+ x f*(x). Does g have a local maximum or minimum at x = 1? Explain your reasoning.(3 points) Determine whether each statement is true or false. ? + 1. If h is a function such that lim h(x) exists, then lim h(x) must also exist. x-+3 x-+ 3+ ? 2. The rational function k(x) = has a vertical asymptote at x = -5, and (x + 5)2 lim k(x) does not exist, but it is still correct to say that lim k(x) = co. x--5 x--5 ? 3. If (x) is function such that lim f(x) and lim (x) both exist, then lim f(x) must x-+7 x-7 x-+7 also exist. ? 4. If m is a function such that lim m(x) = 3, then we must have m(1) = 3. x++1 ? 5. If f and g are functions such that lim f(x) = lim g(x), then f and g must have the X-+0 x+0 same y-intercept. ? 6. If f and g are two functions such that f(x) = g(x) everywhere except x = 2, then for all values of a, then either lim f(x) = lim g(x) or neither limit exists. x - a x -+aQ1 (9 points) Let f(x) if x > 0 x2+1, if x 50 (a) Sketch the graph of the function f. (b) Find the range of f . Express the answer using interval notation. (c) Using the graph from part (a), find each of the three limits given below, if it exists. If the limit does not exist, indicate whether it tends to co or -co, or neither. lim f(x) lim f(x) lim f(x) x+0 x-0* x+0