Exam 3: Applications of the Derivative

Sketch labeled graphs of each function $f ( x ) = \ln 2 x + 1$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^ { \prime \prime}$

(Essay)

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Question 81

Find the critical points of $f ( x ) = 6 x ^ { 4 } - 16 x ^ { 3 } - 24 x ^ { 2 } + 24 x$

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Question 82

Find $\lim _ { x \rightarrow 0 ^ { + } } \frac { e ^ { 4 x } } { x ^ { 2 } }$

(Multiple Choice)

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Question 83

Find the point(s) on the curve $y = x ^ { 2 }$ that is closest to the point (0, 3).

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Question 84

Sketch labeled graphs of each function $f ( x ) = ( x - 1 ) ( x + 2 )$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^{\prime \prime }$

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Question 85

Sketch labeled graphs of each function $f ( x ) = \ln 2 x + 1$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^ { \prime \prime}$

Find the critical points of $f ( x ) = 6 x ^ { 4 } - 16 x ^ { 3 } - 24 x ^ { 2 } + 24 x$

Find $\lim _ { x \rightarrow 0 ^ { + } } \frac { e ^ { 4 x } } { x ^ { 2 } }$

Find the point(s) on the curve $y = x ^ { 2 }$ that is closest to the point (0, 3).

Sketch labeled graphs of each function $f ( x ) = ( x - 1 ) ( x + 2 )$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^{\prime \prime }$

Limits

Derivatives

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Functions and Precalculus

Filters

Exam 3: Applications of the Derivative

Sketch labeled graphs of each function f(x)=ln⁡2x+1f ( x ) = \ln 2 x + 1f(x)=ln2x+1 by hand. As part of your work make sign charts for the signs, roots and undefined points of f,f′ and f′′f , f ^ { \prime } \text { and } f^ { \prime \prime} f,f′ and f′′

Find the critical points of f(x)=6x4−16x3−24x2+24xf ( x ) = 6 x ^ { 4 } - 16 x ^ { 3 } - 24 x ^ { 2 } + 24 xf(x)=6x4−16x3−24x2+24x

Find lim⁡x→0+e4xx2\lim _ { x \rightarrow 0 ^ { + } } \frac { e ^ { 4 x } } { x ^ { 2 } }limx→0+​x2e4x​

Find the point(s) on the curve y=x2y = x ^ { 2 }y=x2 that is closest to the point (0, 3).

Sketch labeled graphs of each function f(x)=(x−1)(x+2)f ( x ) = ( x - 1 ) ( x + 2 )f(x)=(x−1)(x+2) by hand. As part of your work make sign charts for the signs, roots and undefined points of f,f′ and f′′f , f ^ { \prime } \text { and } f^{\prime \prime }f,f′ and f′′

Limits

Derivatives

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Functions and Precalculus

Filters

Sketch labeled graphs of each function $f ( x ) = \ln 2 x + 1$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^ { \prime \prime}$

Find the critical points of $f ( x ) = 6 x ^ { 4 } - 16 x ^ { 3 } - 24 x ^ { 2 } + 24 x$

Find $\lim _ { x \rightarrow 0 ^ { + } } \frac { e ^ { 4 x } } { x ^ { 2 } }$

Find the point(s) on the curve $y = x ^ { 2 }$ that is closest to the point (0, 3).

Sketch labeled graphs of each function $f ( x ) = ( x - 1 ) ( x + 2 )$ by hand. As part of your work make sign charts for the signs, roots and undefined points of $f , f ^ { \prime } \text { and } f^{\prime \prime }$