Question

23. [-16 Points] DETAILS LARCALCET7 4.4.028.EP. Consider the following function. f(x) = 3 sin(x) + 3 cos(x), [0, 27) Find f'(x). f'(x) = Find f'(x). f"(x) = Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.) (x, y) = (smaller x-value) (x, y) = (larger x-value) Describe the concavity. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) concave upward concave downward

Answer 1

[0, 25 - Given fin) = 3 Sina+ 30 30 fix = 3.d (sinn) + 3 & (Losn)) an du f(x) = 3 cose 3 sinal f" (as - 3.d (sina) 3.d (osa) dh an 18" (al- -3 sina – 3 cosa for -) f"(x)=0 Inflection points : च) - 3 sina - 3 losa=0 Sinn = -losa tana = -1 n = I1 + I, 31 + I и nê 39 711 и Inflection foints) & (21) = n = 30 - 3. Sin ) - 3 Cos () - 3 J2 3 T2 117 () -3 Sin) = 360(RED = )

(ny) (3117 So, Inflection points 209.00) -) f(x)=-3 Sinn -3 osaa - [Sinn. 1 / + losno -347 Sin (2+1) Ч 79 = f(x) 19 362 + 3 Elu 4T/ч f"C). allt 다. n =D الو - from graph Thor fin) to Concave upward : fin) > 0 -) at (3/4 , 77/4 fino to Concave downward : {"calco ut Co, ) o ( 27