A function satisfies f0 3 and f2 e2 2 and f3 e3 figure

Question

a) Show that the fllowing fuction is continuous when k = 5\2, then sow that f is not differntiable at x=2.

f(x) = 6x - 2 for x is less than or equal to 2

kx² for x is greater than 2

b) Show that f(x) is continuous and differntiable at x=1

f(x) = 2x for x is greater than 1

x² +1 for x is less than or equal to 1

c) A function satisfies f(0) = 3 and f(2) = e² + 2 and f'(3) = e³, figure out a function f(x) that happenes to satisfy these conditions, then find the line tangent to the curve graph of f(x) when x = 3, sketch the graph of f(x)and the tangent line