21. Let f(x)=2π​1​e2−x2​. Which of the following statements are true? (2 marks) a) x=0,x=2​ and x=−2​ are critical point

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21. Let f(x)=2π​1​e2−x2​. Which of the following statements are true? (2 marks) a) x=0,x=2​ and x=−2​ are critical points of f b) f attains a maximum value at x=0 c) f has a point of inflection at x=1 and x=−1 d) f is concave upward when x>1 c) y=0 is a horizontal asymptote for f 22. Let f(x)=4x31​+x3. Which of the following statements are true? ( 2 marks) a) x=−1 and x=0 are critical points of f b) f is always increasing c) f has a point of inflection at x=0 d) f is concave downward on (0,∞) e) f′′(x) does not exist at x=0 23. The length of a rectangle is increasing at the rate of 2 meters per socond, while the width is increasing at the rate of 1 meter per second. When the length is 4 meters and the width is 3 meters, how fast is the area of the rectangle increasing? a) 5 m2/s b) 6 m2/s c) 10 m2/s d) 11 m2/s e) None of the above 24. A ladder 10 meters long is leaning against a wall, with the top of the ladder 6 meters above the ground. If the top of the ladder is sliding down the wall at 4 meters per second, how fast is the bottom of the ladder moving away from the wall? a) 2 m/s b) 4 m/s c) 5 m/s d) 8 m/s e) None of the above