MAT 211 - Spring 2025 Exam 2 Review Dr. Himali Gammanpila 1. Find the derivative. (a) f(x)=5x6-2x-3x+2 4 (b) f(x) = 5x6-2x-3x+2+ 4 2 +4√√x- + √x 2 3x3 (c) y = (x4 +3x² - 2)(x4 + 3x² - 2) (d) y = (x³-7)(3x² - 7x+1) x3 (e) y = 1 - x2 (f) y=√√√x3+3x+5 (g) y = (x5+5x2+3x+ -2) 5 (h) y= 1 (x7 +11x5+3)³ (i) y = (x³-7)5(3x² - 7x+1)3 (j) f(x) = 3x (x2+5)8

2sin(2x)=√3

Let f(x)=2x+1 and g(x)=2x2-1 a. f(2) b. g(-3)

Differentiate the function f(x) =x*(1– 4x?)3. Express your answer in simplified, factored form.

a) Select a point on the graph of y = −x² + 2x³ + 13x² − 14x − 24, where the roller coaster is going up and evaluate The First Derivative i. ii. b) Select a point on the graph of y = -x + 2x³ + 13x² − 14x − 24, where the roller coaster is down and evaluate The First derivative The Second Derivative ii. The Second Derivative c) At the highest, or lowest point of the coaster, the first derivative is zero. Does that mean that the second derivative at that point is zero? Explain using correct mathematical language and diagrams/graphs, and examples.

Please help me slove this and chose the correct answer.