Question

Use the Constant Rule, the Constant Multiple Rule, and the Sum Rule to find $h^{\prime}(1)$ given that $f^{\prime}(1)=3$. $$ \text { (a) } h(x)=f(x)-2 \quad \text { (b) } h(x)=2 f(x) $$ $$ \text { (c) } h(x)=-f(x) \quad \text { (d) } h(x)=-1+2 f(x) $$

Name: Problem 59, Chapter 2: Calculus an Applied Approach
Uploaded: 2021-06-13T23:07:28-08:00
Duration: 2 min 13 s
Channel: Lauren Shelton
Description: Use the Constant Rule, the Constant Multiple Rule, and the Sum Rule to find h^'(1) given that f^'(1)=3. (a) h(x)=f(x)-2 (b) h(x)=2 f(x) (c) h(x)=-f(x) (d) h(x)=-1+2 f(x)

   Use the Constant Rule, the Constant Multiple Rule, and the Sum Rule to find $h^{\prime}(1)$ given that $f^{\prime}(1)=3$.
$$
\text { (a) } h(x)=f(x)-2 \quad \text { (b) } h(x)=2 f(x)
$$
$$
\text { (c) } h(x)=-f(x) \quad \text { (d) } h(x)=-1+2 f(x)
$$

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 2, Problem 59

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Solved by Expert Lauren Shelton

06/13/2021

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Use the Constant Rule, the Constant Multiple Rule, and the Sum Rule to find $h^{\prime}(1)$ given that $f^{\prime}(1)=3$. $$ \text { (a) } h(x)=f(x)-2 \quad \text { (b) } h(x)=2 f(x) $$ $$ \text { (c) } h(x)=-f(x) \quad \text { (d) } h(x)=-1+2 f(x) $$

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Key Concepts

Constant Multiple Rule

The Constant Multiple Rule tells us that if a function f(x) is multiplied by a constant c, the derivative of the resulting function is c times the derivative of f(x). This rule allows us to simplify differentiation when functions are scaled by constants.

Constant Rule

The Constant Rule states that the derivative of a constant function, that is, a function that always outputs the same value regardless of the input, is zero. This is because constants do not change and therefore have no rate of change.

Sum Rule

The Sum Rule for derivatives states that the derivative of a sum (or difference) of functions is equal to the sum (or difference) of their individual derivatives. This rule makes it easier to differentiate more complex functions that can be decomposed into simpler parts.

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