Sophie S

University of Southern California
Physics/Math tutor

Biography

I hold a B.Sc in electrical engineering and I have informal experience in tutoring physics (intro level kinematics, E&M, optics & modern physics) and maths (calculus).

Education

BS Electrical Engineering
University of Southern California

Educator Statistics

Numerade tutor for 6 years
281 Students Helped

Topics Covered

Understanding Reflection and Refraction of Light: A Comprehensive Guide
Calculating Electrical Power: Resistance and EMF
Master Direct Current Circuits with Our Expert Guide
Electromagnetic Induction: Understanding the Science and Applications
Master the Fundamentals of Physics: Learn Physics Basics
Mastering Motion: Achieving Efficiency Along a Straight Line
Motion in 2d or 3d
Unlock the Secrets of Fluid Mechanics with Our Expert Guide
Understanding Electromagnetic Waves: A Comprehensive Guide
Exploring the World of Derivatives: A Comprehensive Guide
Stand Out with Differentiation Strategies | Boost Your Business
Applications of the Derivative
Discovering the Fundamentals: Newton's Laws of Motion Explained
Mastering Newton's Laws: Tips for Applying Them Effectively
Find Your Dream Job: Discover the Best Work Opportunities
Unlock the Power of Kinetic Energy: Boost Your Efficiency Today
Unlocking the Power of Potential Energy: Discover the Benefits
Save Energy and Money with Effective Conservation Techniques
Unlocking the Power of Electric Potential: Exploring its Benefits

Sophie's Textbook Answer Videos

05:07
Calculus for AP

In Exercises $1-20$ , find the derivative.
$$
y=2^{x^{3}}
$$

Chapter 3: DIFFERENTIATION
Section 9: Derivatives of General Exponential and Logarithmic Functions
Sophie S
08:51
Calculus of a Single Variable

In Exercises $17-42,(\text { a })$ find the critical numbers of $f(\text { if any }),(b)$ find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
$$
f(x)=(x-1)^{2}(x+3)
$$

Chapter 3: Applications of Differentiation
Section 3: Increasing and Decreasing Functions and the First Derivative Test
Sophie S
06:36
Calculus of a Single Variable

In Exercises $17-42,(\text { a })$ find the critical numbers of $f(\text { if any }),(b)$ find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
$$
f(x)=(x+2)^{2}(x-1)
$$

Chapter 3: Applications of Differentiation
Section 3: Increasing and Decreasing Functions and the First Derivative Test
Sophie S
05:47
Calculus of a Single Variable

In Exercises $17-42,(\text { a })$ find the critical numbers of $f(\text { if any }),(b)$ find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
$$
f(x)=5-|x-5|
$$

Chapter 3: Applications of Differentiation
Section 3: Increasing and Decreasing Functions and the First Derivative Test
Sophie S
05:58
Calculus of a Single Variable

In Exercises $17-42,(\text { a })$ find the critical numbers of $f(\text { if any }),(b)$ find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
$$
f(x)=\left\{\begin{array}{ll}{-x^{3}+1,} & {x \leq 0} \\ {-x^{2}+2 x,} & {x>0}\end{array}\right.
$$

Chapter 3: Applications of Differentiation
Section 3: Increasing and Decreasing Functions and the First Derivative Test
Sophie S
07:43
Calculus of a Single Variable

In Exercises $43-50$ , consider the function on the interval $(0,2 \pi) .$ For each function, (a) find the open interval(s) on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results.
$$
f(x)=\sin x \cos x+5
$$

Chapter 3: Applications of Differentiation
Section 3: Increasing and Decreasing Functions and the First Derivative Test
Sophie S
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