MAT 122 Quiz: MAT 122 SBU Quiz 5 Solution

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 122
• Professor: All

Document Summary

Question 1: let f (x) = 5x2 + 3x . 2 x . (a) find the derivative f (x). f (x) = d dx (cid:18)5x2 + 3x . = 5 2x + 3 1 2 ( 1)x 2. = 10x + 3 + 2x 2 = 10x + 3 + dx. 2 x2 (b) find the second derivative f (x). f (x) = (f (x)) d dx d d dx (cid:0)10x + 3 + 2x 2(cid:1) d (10x) + (3) + d dx (x) + dx d dx dx. 4 x3 dx d (2x 2) d dx (x 2) Question 2: at what values of t does the graph of g(t) = 2 t lines? t. The derivative gives the value of the slope of the tangent line, so to nd where the function g has horizontal tangent lines (that is, slope zero tangent lines), we need to solve the equation g (t) = 0.