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Is the statement true or false? Give an explanation for your answer. If $f^{\prime}(2)=3.1$ and $g^{\prime}(2)=7.3,$ then the graph of $f(x)+g(x)$ has slope 10.4 at $x=2$.

Name: Problem 110, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-16T17:56:23-08:00
Duration: 1 min 11 s
Channel: Gregory Higby
Description: Is the statement true or false? Give an explanation for your answer. If f^'(2)=3.1 and g^'(2)=7.3, then the graph of f(x)+g(x) has slope 10.4 at x=2.

   Is the statement true or false? Give an explanation for your answer.
If $f^{\prime}(2)=3.1$ and $g^{\prime}(2)=7.3,$ then the graph of $f(x)+g(x)$ has slope 10.4 at $x=2$.

Calculus Single Variable

Deborah… 7th Edition

Chapter 3, Problem 110

Instant Answer

Solved by Expert Gregory Higby

04/16/2021

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e., $h(x) = f(x) + g(x)$. Show more…

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Is the statement true or false? Give an explanation for your answer. If $f^{\prime}(2)=3.1$ and $g^{\prime}(2)=7.3,$ then the graph of $f(x)+g(x)$ has slope 10.4 at $x=2$.

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Key Concepts

Derivative

The derivative of a function at a given point represents the instantaneous rate of change or the slope of the tangent line to the function's graph at that point. It provides crucial insight into how the function is behaving locally around that point.

Sum Rule for Derivatives

The sum rule for derivatives states that the derivative of the sum of two functions is equal to the sum of their derivatives. This means that if you know the derivatives of two functions at a specific point, the derivative of their sum at that same point can be obtained by simply adding the individual derivatives.

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