Horizontal tangent line: The first order derivative of a function gives the slope of the tangent of the function. The slope of horizontal line is zero.If the slope of tangent line is zero then the tangent line is called horizontal tangent line.

(a)

Given function is,

$f(x)= 3x+3sin x$

Differential with respect to x

$f'(x)=3+3cos x$

For horizontal tangent line, f'(x)=0

3+ 3 cos x= 0

⇒3 cos x=-3

⇒cos x=-1

⇒x = 180° $=\pi$

Therefore the value of x= $\pi$

(b)

Given that, the slope is 3.

Then,f'(x)=3

3+ 3 cos x= 3

⇒3 cos x= 3-3

⇒cos x=0

⇒x = 90° $=\frac{\pi}{2}$

Therefore the value of x $=\frac{\pi}{2}$

5 0

3 years ago

Kim sold christmas pies for 5.00$ each. She earned 156 how many pies she sold also let x repersent the number of pies, x, kim so

MA_775_DIABLO [31]

Answer: 31.2 pies

Step-by-step explanation:

Kim sold pies for $5.00 each and earned $156 from doing so.

The number of pies she sold to get to this was x pies.

The formula for doing so is therefore:

5 * x pies = 156

5x = 156

x = 156 / 5

= 31.2 pies

4 0

3 years ago

Answer correctly for brainliest and also a thanks ! Don't answer if you don't know it please !

Drupady [299]

The answer is B for increase of one year the events increase by 0.5

You can do this by using the eqn

y=0.5x-1.3
y=0.5(15)-1.3
y = 7.5-1.3
y = 6.2

y=0.5(16)-1.3
y=8-1.3
y=6.7

6.7-6.2 = 0.5

5 0

3 years ago