Question

1) Find the absolute extremum values of f(x) = x^2 - 4x + 16 over the interval [1, 4]. [2 marks] 2)The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume decreases when the radius is 2 m. [2 marks] 3)Verify Rolle's Theorem for the function f(x) = 2x^2 + 6 defined over the interval [-6, 6]. Justify your answer. [2 marks] 4) Determine the following for the function f(x) = (2x^3 / 3) - 8x^2 + 32x + 4: (i) intervals where f is increasing or decreasing, (ii) local minima and maxima of f, (iii) intervals where f is concave up and concave down, and [2 marks] (iv) the inflection points of f. 5) The position vector of a particle is given by s(t) = 2t^2 - 2t + 5. Find the time at which the instantaneous velocity equals the average velocity over the time interval [1, 6]. [2 marks]

          1) Find the absolute extremum values of f(x) = x^2 - 4x + 16 over the interval [1, 4]. [2 marks]
2)The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume decreases when the radius is 2 m. [2 marks]
3)Verify Rolle's Theorem for the function f(x) = 2x^2 + 6 defined over the interval [-6, 6]. Justify your answer. [2 marks]
4) Determine the following for the function f(x) = (2x^3 / 3) - 8x^2 + 32x + 4:
(i) intervals where f is increasing or decreasing,
(ii) local minima and maxima of f,
(iii) intervals where f is concave up and concave down, and [2 marks]
(iv) the inflection points of f.
5) The position vector of a particle is given by s(t) = 2t^2 - 2t + 5. Find the time at which the instantaneous velocity equals the average velocity over the time interval [1, 6]. [2 marks]

1) Find the absolute extremum values of f(x) = x^2 - 4x + 16 over the interval [1, 4]. [2 marks]
2)The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume decreases when the radius is 2 m. [2 marks]
3)Verify Rolle's Theorem for the function f(x) = 2x^2 + 6 defined over the interval [-6, 6]. Justify your answer. [2 marks]
4) Determine the following for the function f(x) = (2x^3 / 3) - 8x^2 + 32x + 4:
(i) intervals where f is increasing or decreasing,
(ii) local minima and maxima of f,
(iii) intervals where f is concave up and concave down, and [2 marks]
(iv) the inflection points of f.
5) The position vector of a particle is given by s(t) = 2t^2 - 2t + 5. Find the time at which the instantaneous velocity equals the average velocity over the time interval [1, 6]. [2 marks]

Added by Christopher C.

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