The functions f(x) and g(x) are differentiable. The function h(x) is defined as: h(x) = g(x) – f(x) If f(2) = 5, f′(2) = –1, g(2) = –7, and g′(2) = 3, what is h′(2)? Simplify any fractions. h′(2) = ____

Identify Derivative of h(x): Identify the derivative of h(x) using the properties of derivatives. Since h(x) = g(x) – f(x), by the linearity of the derivative, we have h′(x) = g′(x) – f′(x).Substitute Values for h′(2): Substitute the given values into the derivative of h(x) to find h′(2). We have f′(2) = –1 and g′(2) = 3, so h′(2) = g′(2) – f′(2) = 3 - (–1) = 3 + 1.Calculate h′(2): Calculate the value of h′(2). h′(2) = 3 + 1 = 4.

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The functions $f(x)$ and $g(x)$ are differentiable. The function $h(x)$ is defined as: $\newline$ $h(x) = g(x) - f(x)$ $\newline$ If $f(2) = 5$ , $f'(2) = -1$ , $g(2) = -7$ , and $g'(2) = 3$ , what is $h'(2)$ ? $\newline$ Simplify any fractions. $\newline$ $h'(2) =$ ____

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Algebra 2

Transformations of absolute value functions

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Q. The functions

f(x)

and

g(x)

are differentiable. The function

h(x)

is defined as:

\newline

h(x) = g(x) - f(x)

\newline

f(2) = 5

f'(2) = -1

g(2) = -7

, and

g'(2) = 3

, what is

h'(2)

\newline

Simplify any fractions.

\newline

h'(2) =

____

Identify Derivative of $h(x)$ : Identify the derivative of $h(x)$ using the properties of derivatives. $\newline$ Since $h(x) = g(x) - f(x)$ , by the linearity of the derivative, we have $h'(x) = g'(x) - f'(x)$ .
Substitute Values for $h'(2)$ : Substitute the given values into the derivative of $h(x)$ to find $h'(2)$ . We have $f'(2) = -1$ and $g'(2) = 3$ , so $h'(2) = g'(2) - f'(2) = 3 - (-1) = 3 + 1$ .
Calculate $h'(2)$ : Calculate the value of $h'(2)$ . $h'(2) = 3 + 1 = 4$ .