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sattari [20]
2 years ago
14

(a)Use differentiation to find the minimum value of f(x)= 3x^2 - 5x + 10 and the value(s) of x for which this minimum occurs.

Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
3 0

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.

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Approximate the zeros of the function. Round to the nearest tenth if necessary. f(x) = 4x^2 + 4x - 35. Explain each step on how
svet-max [94.6K]
4x²+4x-35=0
factor: (2x+7)(2x-5)=0
2x+7=0, or 2x-5=0
2x=-7 or 2x=5
x=-3.5 or x=2.5

I don't see any rounding necessary in this case. 

when you factor ax²+bx+c, you take the two factors of a and the two factors of c, one factor of a times one factor of c, the other factor of a times the other factors, the sum of the two products make b.
in this case, the factors of 4 is 2 and 2, the factors of -35 is -5 and 7. I line them up in the following way:
2    -5

2      7
then I multiple them diagonally, the top left 2 multiplying the bottom right 7=14, and the other 2 multiplying -5=-10, 14 and -10 make a sum of 4.

if you don't get the desired sum, switch the factors up and down till you have the right combination. Note: Do not switch left and right. 

I hope this makes sense to you.
8 0
3 years ago
Use the Perfect Square Trinomial and provide the first step to calculating 382 without a calculator.
dusya [7]

Answer:

(40-2)^2

Step-by-step explanation:

Given: (38)^2

To find: the correct option

Solution:

A binomial polynomial is a polynomial consisting of two terms.

A trinomial polynomial is a polynomial consisting of three terms.

On multiplying a binomial (x-y) to itself, a perfect square trinomial (x-y)^2 is obtained.

Here, 38=40-2

So, (38)^2=(38)(38)=(40-2)(40-2)=(40-2)^2

Here, (40-2) is a binomial and it is multiplied to (40-2) to get a perfect square trinomial (40-2)^2

7 0
3 years ago
What is the slope of the line shown?
Papessa [141]

Answer:

The slope of the line shown is 2

4 0
3 years ago
5x + 3 = 23 5. 4 = 3a – 14 6. 2y + 5 = 19 i need help with this equation
mrs_skeptik [129]

Answer:

Step-by-step explanation:

    5x + 3 = 23 x=4

5. 4 = 3a – 14 a=6

6. 2y + 5 = 19 y=7

6 0
3 years ago
Charlotte divided a whole pizza into 4 pieces. one piece formed a straight angle. one formed a right angle. two pieces formed ac
Minchanka [31]
You have to draw a pie graph.

The first piece (with the straight angle) cuts the pie in half. 

The second piece cuts the remaining half in halves (making a quarter).

The third and fourth pieces are the same as each other. So they must each have an angle of 45 degrees. Each of these is an eighth of the total pie.

Should be fairly easy. Good luck!
7 0
3 years ago
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