The function h is continuous on the closed interval [-2, 5] and differentiable on the open interval (-2, 5) . If f (-2) = 3 and f (5) =-11, which of the following statements could be false?

There exists a c on the interval (-2, 5) such that f'(c) = 0.

There is an absolute maximum value on the interval [-2, 5]

There exists a con on the interval (-2, 5) such that f(c) = 0.

There exists a c on the interval (-2, 5) such that f'(c) = -2.

h(x) is a differentiable function that contains the points (2, -5) and (5, 4). Which of the following must be true?

h(x) is increasing over the interval (2, 5)

h(x) intercepts the x – axis at 113

h'(c) =0 for some c in the interval (-5, 4).

The function f is continuous and differentiable. The table gives selected values of f. Which statement must be true?

There is a 'c' such that f′(c) = 0

The function f is continuous and differentiable for 0 ≤ x ≤ 8. If g(0) = 7 and g(8) = -9, which could be false?

There is a 'c' (0<c<8), where g′(c) = -1

There is a 'c’ (0<c< 8), where g(c) = -1

There is a 'c' (0<c<8), where g(c) = -2

There is a 'c' (0<c<8), where g′(c) = -2

EVT, MVT, IVT, and Rolle's Theorem Review

Authored by Laurell Wiersma

Mathematics

11th Grade - University

CCSS covered

Used 13+ times

EVT, MVT, IVT, and Rolle's Theorem Review

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Let f be the function defined by f(x) = x³+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3].

√(2/3)

√(7/3)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If f(x)=x³, at what point on the interval 0<x<3 is the tangent to the curve parallel to the secant line for this interval?

√3

√3/3

1/3

If f(x)=sin(x/2), at what point on the interval π/2<x<3π/2 is the tangent to the curve parallel to the secant line for this interval?

2π/3

3π/4

5π/6

On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x³-3x²+12 occurs at x =

0 and 3

0 and 2

-2 and 0

Suppose that f is differentiable for all reals. For x in the interval (-5, 0), suppose that f'(x)<0. For x in the interval (0, 5), suppose that f'(x) >0. Then at x = 0 it must be true that f has

an inflection point

an absolute maximum

an absolute minimum

a relative minimum

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Suppose that f is differentiable for all reals. For x in the interval (-∞, 4), suppose that f'(x)>0. For x in the interval (4, ∞), suppose that f'(x) <0. Then at x = 4 it must be true that f has

no extrema

a relative minimum

an absolute maximum

an absolute minimum

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed?

g(0) = 0

g'(c)= 0 for some c in (-1,3)

g'(c)= 4 for some c in (-1, 3)

g(c)= 4 for some c in (-1, 3)

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EVT, MVT, IVT, and Rolle's Theorem Review

Let f be the function defined by f(x) = x³+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3].

If f(x)=x³, at what point on the interval 0<x<3 is the tangent to the curve parallel to the secant line for this interval?

If f(x)=sin(x/2), at what point on the interval π/2<x<3π/2 is the tangent to the curve parallel to the secant line for this interval?

On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x³-3x²+12 occurs at x =

Suppose that f is differentiable for all reals. For x in the interval (-5, 0), suppose that f'(x)<0. For x in the interval (0, 5), suppose that f'(x) >0. Then at x = 0 it must be true that f has

Suppose that f is differentiable for all reals. For x in the interval (-∞, 4), suppose that f'(x)>0. For x in the interval (4, ∞), suppose that f'(x) <0. Then at x = 4 it must be true that f has

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed?

The function h is continuous on the closed interval [-2, 5] and differentiable on the open interval (-2, 5) . If f (-2) = 3 and f (5) =-11, which of the following statements could be false?

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?
I. g has at least one horizontal tangent line.
II. g has at least 2 zeros.
III. For some c in the interval (3, 6), f'(c) = -7/3.

If f(x) = x³ + 1 then there exists a number c in the interval (0, 1) that satisfies the conclusion of the Mean Value Theorem. Which of the following could be c ?

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EVT, MVT, IVT, and Rolle's Theorem Review

Let f be the function defined by f(x) = x3+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3].

If f(x)=x3, at what point on the interval 0<x<3 is the tangent to the curve parallel to the secant line for this interval?

If f(x)=sin(x/2), at what point on the interval π/2<x<3π/2 is the tangent to the curve parallel to the secant line for this interval?

On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x3-3x2+12 occurs at x =

Suppose that f is differentiable for all reals. For x in the interval (-5, 0), suppose that f'(x)<0. For x in the interval (0, 5), suppose that f'(x) >0. Then at x = 0 it must be true that f has

Suppose that f is differentiable for all reals. For x in the interval (-∞, 4), suppose that f'(x)>0. For x in the interval (4, ∞), suppose that f'(x) <0. Then at x = 4 it must be true that f has

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed?

The function h is continuous on the closed interval [-2, 5] and differentiable on the open interval (-2, 5) . If f (-2) = 3 and f (5) =-11, which of the following statements could be false?

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?I. g has at least one horizontal tangent line.II. g has at least 2 zeros.III. For some c in the interval (3, 6), f'(c) = -7/3.

If f(x) = x3 + 1 then there exists a number c in the interval (0, 1) that satisfies the conclusion of the Mean Value Theorem. Which of the following could be c ?

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Popular Resources on Wayground

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Let f be the function defined by f(x) = x³+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3].

If f(x)=x³, at what point on the interval 0<x<3 is the tangent to the curve parallel to the secant line for this interval?

On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x³-3x²+12 occurs at x =

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?
I. g has at least one horizontal tangent line.
II. g has at least 2 zeros.
III. For some c in the interval (3, 6), f'(c) = -7/3.

If f(x) = x³ + 1 then there exists a number c in the interval (0, 1) that satisfies the conclusion of the Mean Value Theorem. Which of the following could be c ?