For your response posts [2], you must do the following: - Review the explanation given by your peers to describe their problem solving strategies. Your comments may focus on the following: a How did they describe steps to make their explanation clear? a What additional details could they have included? a What details did they include that you may not have? a What changes would you make to your initial post to make it clearer? - Reply to at least two different classmates outside of your own initial post thread. - Complete the two response posts by Sunday at 11:59 pm. of your local time zone. - Demonstrate more depth and thought than simply stating that "I agree" or "You are wrong." Guidance is provided for you in each discussion prompt. For x = 10 f(x) = sqrt(10(x)) + 14 1/2(10) + 19 = 24 sqrt(10(10)) + 14 = 24 Plugging 10 in for the value of x on both equations will net the same result, 24. The left hand and right hand limits are both equal to 24 Now that we know both functions to be continuous we can determine the differentiability of each side of the function. (f(10+h) - f(10))/h (1/2(10+h) + 19) - (1/2(10) + 19))/h (5+19) - (5+19) = 0 ((sqrt(10+h) +14) - (sqrt(10) + 14))/h (sqrt(10) + 14) - (sqrt(10) + 14) = 0 Both left hand and right hand differentials are equal at 0 therefor f(x) is differentiable and continuous at x = 10