Consider the equation below. (If an answer does not exist, enter DNE.)f(x) = e9x + e−x(a)Find the interval on which f is increasing. (Enter your answer using interval notation.)(−ln(3)5​,∞) Find the interval on which f is decreasing. (Enter your answer using interval notation.)(−∞,−ln(3)5​) (b)Find the local minimum and maximum values of f.local minimum value −ln(9)10​ local maximum value DNE (c)Find the inflection point.(x, y) =  DNE Find the interval on which f is concave up. (Enter your answer using interval notation.)(−∞,∞) Find the interval on which f is concave down. (Enter your answer using interval notation.

Consider the following. (If an answer does not exist, enter DNE.)f(x) = 9 sin(x) + 9 cos(x),    0 ≤ x ≤ 2𝜋(a)Find the interval(s) on which f is increasing. (Enter your answer using interval notation.) (b)Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.) (c)Find the local minimum and maximum values of f.local minimum value local maximum value

Use the graph to determine the open intervals over which  is increasing, decreasing, or constant, then determine all the local minimum and maximum values on the graph.a.)Increasing on Decreasing on Local minimum is 1 at Local maximum is -1 at b.)Increasing on Decreasing on Local minimum is 2 at Local maximum is 6 at c.)Increasing on Decreasing on Local minimum is 1 at Local maximum is -1 at d.)Increasing on Decreasing on Local minimum is 2 at Local maximum is 6 at

he graph of a function f is given. Use the graph to estimate the following.(a) All the local maximum and minimum values of the function and the value of x at which each occurslocal maximum     (x, y) = 0,12 local minimum      (x, y) = −9,−6 (smaller x-value)local minimum (x, y) = 6,3 (larger x-value)(b) The intervals on which the function is increasing and on which the function is decreasing. (Enter your answers using interval notation.)increasing     (−∞,−9)∪(0,6) decreasing     (0,6)

Partially Correct(d): Answer all the questions before selecting Check.Try one last timeBelow is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.y246810-2-4-6-8-10x2468-2-4-6-8-10Use the graph to answer the following questions.(a) Over which intervals is the function decreasing? Choose all that apply.−−∞, 8−−8, 1−1, 5−8, 55, ∞(b) At which x-values does the function have local maxima? If there is more than one value, separate them with commas.1(c) What is the sign of the function's leading coefficient? (d) Which of the following is a possibility for the degree of the function? Choose all that apply.456789

Suppose f '' is continuous on (−∞, ∞).(a) If f '(3) = 0 and f ''(3) = −5, what can you say about f ?At x = 3, f has a local maximum.At x = 3, f has a local minimum.    At x = 3, f has neither a maximum nor a minimum.More information is needed to determine if f has a maximum or minimum at x = 3.(b) If f '(4) = 0 and f ''(4) = 0, what can you say about f ?At x = 4, f has a local maximum.At x = 4, f has a local minimum.    At x = 4, f has neither a maximum nor a minimum.More information is needed to determine if f has a maximum or minimum at x = 4.