Problem (1) (14 points) Given function f(x)=x²-x+2. (a) Find z and y intercepts. (b) Find the critical values of f. (c) Find the local maximum and minimum (if there is any).

(d) Where is function f(x) increasing? Where is function f(x) decreasing? (e) Where is function f(x) concave up? Where is function f(x) concave down? (f) Find the equation of the tangent line at (2,-4). (g) Sketch the graph of f on [-3, 3].