All categories

3 years ago

Use both the first and second derivative tests to show that f(x) = 3x2 − 6x + 1 has a relative minimum at x=1.

Mathematics

1 answer:

Vlada [557]3 years ago

8 0

Step-by-step explanation:

Given: f(x) = 3x^2 − 6x + 1. x ∈ (-∞, ∞)

now differentiating f(x) w.r.t. x we get

f'(x) = 6x-6

equating it 0 we get

x = 1, which is a critical point

Now using second derivative test to check relative maxima or minima

f''(x) = 6 >0

⇒ x=1 is a relative minima.

also, x=1 f(1) = 3-6+1 = -2

You might be interested in

Work out the volume of this cylinder. Give your answer rounded to the nearest whole number.

LUCKY_DIMON [66]

Answer:

31793 cm^3

Step-by-step explanation:

Equation

Volume = $\pi$ * r^2 * h

Givens

d = 2*r

d = 30

r = 15

h = 45

$\pi$ = 3.14

Solution

V = 3.14 * 15^2 * 45

V = 31793 rounded.

4 0

3 years ago

The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?

patriot [66]

Answer:x=-1

Step-by-step explanation:

4 0

3 years ago

What is the degree measure of ACD

kupik [55]

Answer:

the answer is 75 because the measure of the arc is 75. pls mark as brainliest:)

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

Helen wants to find the surface area of the solid pictured on the left, so she constructs a net of the solid pictured on the rig

lana [24]

Answer:

Helen’s net is correct because she reorganized the solid as a triangular prism.

This is because the net has a rectangular base and 4 triangular sides.

Step-by-step explanation:

Rectangular SA one side+1 = 30 x 9 = 270 + 1s= 270 x 2 =540sq^2

Rectangular side one side +1 = 18 x 9 = 162 +1s = 162 x 2 = 324sq^2

2 x 2 triangular sides either end = 4/3 x 15 x 27.3 + 18 x 30.9 = 409.5 (x2) = 819sq^2

=864 + 360

Pyramid area = 1236.71sq^2

Volume = V=1620^3

3 0

3 years ago

Read 2 more answers

*FIRST ANSWER GETS BRAINLIEST*

svet-max [94.6K]

The other solution to the equation is -3.

Step-by-step explanation:

Given equation is;

5x²+bx+12=0

One solution is -4/5

We will put this solution in Eqn to get the value of b first,

$5(\frac{-4}{5})^2+b(\frac{-4}{5})+12=0\\5(\frac{16}{25})+(\frac{-4b}{5})+12=0\\\frac{16}{5}-\frac{-4b}{5}=-12\\$

Multiplying each term by 5

$5*(\frac{16}{5})-\frac{-4b}{5}*5=-12*5\\16-4b=-60\\-4b=-60-16\\-4b=-76$

Dividing both sides by -4

$\frac{-4b}{-4}=\frac{-76}{-4}\\b=19$

Putting b=19 in given Eqn

5x²+19x+12=0

Here,

a=5 , b=19 , c=12

Using quadratic formula,

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\x=\frac{-(19)\±\sqrt{(19)^2-4(5)(12)}}{2(5)}\\\\x=\frac{-19\±\sqrt{361-240}}{10}\\\\x=\frac{-19\±11}{10}\\$

Either, or,

$x=\frac{-19+11}{10},\ \ \ \ \ \ x=\frac{-19-11}{10}\\x=\frac{-8}{10},\ \ \ \ \ \ \ \ \ x=\frac{-30}{10}\\x=\frac{-4}{5},\ \ \ \ \ \ \ \ \ \ x= -3$

The other solution to the equation is -3.

Keywords: linear equation, quadratic formula

Learn more about quadratic formula at:

#LearnwithBrainly

6 0

3 years ago