CoursHeroTranscribedText: Math 11517 Summer 2023 Written Homework 2 Page 2 of 6 Problem 1: Secant and Tangent Lines of a Piecewise Function (36 points) A piecewise defined function g is given by the formula X2 ix+l ifx4 A partial graph of this function is given below. In this problem, we will find secant and tangent lines to this function. A ,2 71 1 2 3 4 5 6 7 a) (2 points) On the graph above, draw the secant line of g(X) between x : 0 and X : 6. Label this line with a large 5. b) (2 points) Find the slope of the secant line you drew in Part (a). Slope: c) (3 points) Find an equation of the secant line you drew in Part (a). Equation: d) (2 points) On the graph above, draw the line tangent to g(X) at X : 3. Label this line with a large T. Math 11517 Summer 2023 Written Homework 2 Page 3 of 6 e) (2 points) Evaluate g(4)A g(4) : f) (4 points) Use the definition of continuity to verify that g(x) is continuous at x : 4. (Do not use the graph for this part We want to verify that the graph is displayed correctly) , 4 g) (4 points) For x 4* x _ 4 Math 11517 Summer 2023 Written Homework 2 Page 4 of 6 g(X) 7 EM) i) (4 points) For X > 4, find a formula for x 7 4 . SIMPLIFY your result. gm , gm) : x 7 4 j) (4 points) Evaluate Ellw- ng) * 3(4) lim : x>4+ x4 k) (2 points) Use your answers from above to determine if g'(4) exists. Explain. I) (3 points) Find an equation for the line tangent to g(x) at x : 4, if this line exists. If this tangent line does not exist, explain why. Equation