Question

(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.
Let h(x) = f(g(x)). Find
A. h'(1) =
B. h'(2) =
C. h'(3) =

Answer 1

Answer:

sorry po SABOG po ako ngayon eh sénsya po

Answer 2

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

$\mathbf{h(x) = f(g(x))}$

Start by calculating the equations of f(x) and g(x)

Graph f(x)

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

$\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}$

$\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}$

Graph g(x)

The slope of g(x) is: -1/2

So, the equation is:

$\mathbf{g(x) = -\frac 12x}$

For x = 1 and x = 2, we have:

So, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}$

Open brackets

$\mathbf{h(x) = -\frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = -\frac{3}{4}}$

So:

$\mathbf{h'(1) = -\frac{3}{4}}$

$\mathbf{h'(2) = -\frac{3}{4}}$

For x = 3, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}$

$\mathbf{h(x) = \frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = \frac{3}{4}}$

Substitute 3 for x

$\mathbf{h'(3) = \frac{3}{4}}$

Hence, the values of the derivatives are:

$\mathbf{h'(1) = -\frac{3}{4}}$, $\mathbf{h'(2) = -\frac{3}{4}}$ and $\mathbf{h'(3) = \frac{3}{4}}$

Read more about graphed functions at:

brainly.com/question/11804653