MATH 410 Midterm: MATH410_BOYLE-M_FALL1993_0101_MID_EXAM_1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 410
• Professor: All

Document Summary

The take-home questions are worth 20 of these points: (15 points) prove that there is exactly one number x such that. 0 x 1 x4 = 1 x2. and (15 points) let f be the function from r to r which is de ned by the rule. Justify your answer: (15 points) suppose f (x) is a di erentiable function whose graph has a tangent line at the point (1,1) given by the equation y = 2x 1. Suppose h(x) is a di erentiable function whose graph has a tangent line at the point (1,2) given by the equation y = 6x 4. What is an equation for the tangent line to the graph of h(f (x)) at the point with x coordinate equal to 1? (15 points) prove the following ingredient in the proof of the extreme value. Prove that f is strictly increasing on some open interval containing 2.