Question

Calculate the following derivative if f(x) = sin(x) and g(x) = 5x + 4.

Answer 1

Answer:

Rewrite the function as an equation.

y

=

5

x

−

4

Use the slope-intercept form to find the slope and y-intercept.

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The slope-intercept form is  

y

=

m

x

+

b

, where  

m

is the slope and  

b

is the y-intercept.

y

=

m

x

+

b

Find the values of  

m

and  

b

using the form  

y

=

m

x

+

b

.

m

=

5

b

=

−

4

The slope of the line is the value of  

m

, and the y-intercept is the value of  

b

.

Slope:  

5

y-intercept:  

−

4

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

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Choose  

1

to substitute in for  

x

to find the ordered pair.

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Replace the variable  

x

with  

1

in the expression.

f

(

1

)

=

5

(

1

)

−

4

Simplify the result.

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1

The  

y

value at  

x

=

1

is  

1

.

y

=

1

Choose  

0

to substitute in for  

x

to find the ordered pair.

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Replace the variable  

x

with  

0

in the expression.

f

(

0

)

=

5

(

0

)

−

4

Simplify the result.

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−

4

The  

y

value at  

x

=

0

is  

−

4

.

y

=

−

4

Create a table of the  

x

and  

y

values.

x

y

0

−

4

1

1

Graph the line using the slope and the y-intercept, or the points.

Slope:  

5

y-intercept:  

−

4

x

y

0

−

4

1

1

Step-by-step explanation: