1. Let f(x) = x3 + x2. (4 pts each) a) Find a point c satisfying the conclusion of the MVT for f(x) over the interval [ 1,1]. Graph the function, the secant line for the interval, and the tangent line at (c, f(c)). b) Verify Rolle's Theorem for the interval [ 1, 0]. Find d in [ 1, 0] such that f'(d) : 0. Graph the tangent line at (d, f(d)). 2. Use the graph to the right to answer the following questions. Let 0 be the origin. (8 pts) a) On what intervals is f increasing? b) On what intervals is f decreasing? c) On what intervals is f concave up? 3 _____-___ d) On what intervals is f concave down? e) What are the critical points of f? 0 What are the inection points off? g) Which points are relative maxima? h) Which points are relative minima? 3. Complete the following steps for f(t) = t3 6t2 + 4 (14 pts) a) Find f'(t). b) Find the critical points by setting f'(t) : 0 and solving for t. c) Find f\"(t). d) Use the second derivative test to determine if the critical points are local maximum or local minimum (or can't be determined). e) Find points of inection by setting f\"(t) : 0 and solving for t. 0 Determine the intervals on which the function is concave up and concave down. g) Graph the function in Desmos to verify your results