Chapter 5.2, Problem 40E

Let f(z) = x² + 2xy+ 3y+ i(y² + 2xy+ x). • (i) Determine the line along which f is differentiable. Justify your answer. • (ii) Find the derivative of f along the line of differentiability. • (ii) Is f an analytic function? Justify your answer. q4-123191.pdf

V6 5 V6 5 Select an appropriate graph of a twice-differentiable function y=f(x) that passes through the points (-V2,1),| -- .(0,0), 3 '9 3 '9 and (V2 ,1), and whose first two derivatives have the following sign patterns. 12 V6 V6 3 3 OA. ов. Oc. OD. Ay 18 54 Ay 18- -3 3 -18

Question: How are the average rate of change of a function f on the interval [a, a + h] and the secant line through the points (a, f (a)) and (a + h, f (a + h)) on the function f? 2.

How to solve this? g(t)is a differentiable function

show full and complete procedure HANDWRITTEN only

Demand for RNs The following graph gives the total number of help-wanted ads for RNs (registered nurses) in 22 cities over the last 12 months as a function of time t (t measured in months). y y = Mt) t (months) 12 3 6 (a) Explain why N'(t) is positive on the interval (0, 12). N(t) is increasing. N'(t) is increasing. N'(t) is decreasing. O N(t) is decreasing. O N'(t) is not positive. (b) Determine the signs of N"(t) on the interval (0, I) and the interval (I, 12), where I is the point of inflection. Before the point of inflection: O positive negative zero O undefined O cannot be determined After the point of inflection: positive negative zero undefined cannot be determined Locate the point of inflection. t =

Explain with all explanation

A metal plate is heated so that its temperature at a point (x, y) is T(x, y) = x²e2x+3¥). A bug is placed at the point (1, 1). The bug heads toward the point (2, –4). What is the rate of change of temperature in this direction? (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length Consider the direction the bug should head to warm up at the fastest rate. Find the rate of change of temperature in this direction. (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length Consider the direction the bug should head to cool off at the fastest rate. Find the rate of change of temperature in this direction. (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length

Puestion 28- Given function is flx)= x'-me 574* + 574 Compute deivatve. Find the following u» Inteval "of increasing deeteasig. (2) Eatreme values. (3) Interval of Concave up / down. Plat the osiginal (4) graph-