Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z = 0 and find the value of f'(0).

Let f(z) = iz³ + cos(z²) z² +1 i. Find ƒ'(z). ii. Evaluate f'(−2i) and simplify. iii. State the points in the complex plane at which the derivative is undefined. iv. State, giving reasons, whether or not f(z) is entire.

4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and determine where each are 0 and/or do not exist (DNE). If none, write "none". f' = 0: f' DNE: f" = 0: f" DNE: c) E Do a sign analysis on f' and f". d) Find the intervals on which f is increasing and decreasing. Increasing: Decreasing: e) Find the intervals on which f is concave up and concave down. Concave up: Concave down: f) answers as (x, y) points. Find all local maxima, local minima, and inflection points of f. Be sure to write your Local max: Local min: Inflection point(s): -4 -3 -1 g) Sketch the graph of f.

Which of the following pair of functions is linearly independent? (а) еЗx, е(х-3) (b) 4, sin?x + cos?x (c) 2sin2x, sinxcosx (d) sinhx, (e* – e*)