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​Consider a Differentiable Function That Has an X-Intercept of 2

Question 156

Multiple Choice

​Consider a differentiable function ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only that has an x-intercept of 2 and a y-intercept of 4.In the interval ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only , ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only is decreasing and concave down.Which of the following must be true? ​
​I) The Mean Value Theorem is satisfied when ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only .
II) ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only .
III) A tangent approximation of the function for any value in the interval ​Consider a differentiable function   that has an x-intercept of 2 and a y-intercept of 4.In the interval   ,   is decreasing and concave down.Which of the following must be true? ​ ​I) The Mean Value Theorem is satisfied when   . II)    . III) A tangent approximation of the function for any value in the interval   will underestimate the function value. ​ A) ​I only B) ​II only C) ​III only D) ​I and II only will underestimate the function value.


A) ​I only
B) ​II only
C) ​III only
D) ​I and II only

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