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Consider the function f (x) = 22:3 62:2 18:1: + 51.5uchthata: 6 [~2, 5] Which of the following statements is incorrect/false? The maximum value of f is 61. :1: = 1 is a critical point of f. a: = 3 is a critical point of f. The minimum point of f is ( 3, 3). Which of the following statements is true/correct? If a function f is continuous then f is also differentiable. The tangent line at a point on a curve is a straight line that touches the curve at that point. The derivative of a function at a certain point gives us the slope of the line tangent to the function at any point on the graph. Given a function f (m). the derivative of the function f (1:) is dened as lim,Hz MW. provided that limit exists. Consider the function f (x) = 3x2 + 5, find limp-0 f(ath)-f(x) h A. limn-+0 f(ath)-f(2) = limn-+0 3(xth) +5 -(3x2+5) h h 3(x +2xhth? ) +5 -(323+5) B. = limn-+0 h C. = limp-+0 3x2+6ch+3h2+5-3x2+5 h = limn-+0 6ch+3h2 h = limn-+0 h(6x +3h) h = limn-o (6x + 3h) G. lim, f(ath)-f(2) = 6x h Which part of the given solution below is incorrect? D OOOOOOO nmana AWhat is the missing factor in solving the derivative of the function below? D, [(5 "(m2] = -2 (5 _ 734W (2') 28:1:3 21:::3 215."3 283:3 A poster must have a printed area of 320 cm? . It will have top and bottom margins that are 5 cm each. and side margins that are 4 cm each. If all the dimensions of the printed area are at least 15 cm but at most 30 cm. what are the dimensions of the whole poster with the smallest total area? Answer: The dimensions of the whole poster with the smallest total area are length = _ cm width - _ cm length = 20.7 cm length= 31.3 cm length- 30 cm width = 15 cm width = 30.3 cm width - 24 cm Four students were talking about the process of finding the derivative of the function f (x) = x + 2x -5 2x ABBY: "Surely, we can apply the quotient rule in finding the derivative of that function." BRENT: "The function can be simplified as f (a) = a2 - 5, then we can now find f ' (a)." CARL: "We can apply the product rule in finding f' (a) by using the equivalent expression of f (a) which is -(x2 + 2x - 5 2x DIANE: "Another equivalent expression of f (x) is ~x + 1 1 5 -, that's why we can also use the sum rule in finding f ' (a)." 2x Who among the four students give/s a correct statement? O Abby, Carl and Dianne Brent, Abby and Carl Diane, Brent and Abby O Carl, Diane and Brent2n:2 .1. 2 _ a: and y _ T are the same. The derivatives of the functions y = 2 True False Differentiate y= 2 3x-7 O 94 = (3x-7)3 Oy 108 (3x-7)3 O d = 36 (3x-7)4 O y = 72 (3z-7)4