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3 years ago

Given f'(x)=(x-4)(6-2x) find the x-coordinate for the relative minimum of the graph f(x).

1 answer:

5 0

The graph you plotted is the graph of f ' (x) and NOT f(x) itself. 

Draw a number line. On the number line plot x = 3 and x = 4. These values make f ' (x) equal to zero. Pick a value to the left of x = 3, say x = 0. Plug in x = 0 into the derivative function to get

f ' (x) = (x-4)(6-2x)
f ' (0) = (0-4)(6-2*0)
f ' (0) = -24

So the function is decreasing on the interval to the left of x = 3. Now plug in a value between 3 and 4, say x = 3.5

f ' (x) = (x-4)(6-2x)
f ' (3.5) = (3.5-4)(6-2*3.5)
f ' (3.5) = 0.5

The function is increasing on the interval 3 < x < 4. The junction where it changes from decreasing to increasing is at x = 3. This is where the min happens.

So the final answer is C) 3

You might be interested in

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

PLZ HELP MEEEE!!!

LiRa [457]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Quick I need Helpppp!! Triangle EFT is congruent to triangle JKL. What is KL, in units

Serjik [45]

Answer:

KL = 6 units.

Step-by-step explanation:

Congruent means the same or similar.

Hope this helps!

6 0

3 years ago

Solve this equation 5(-7x-3)- 8x=-230

Brut [27]

Simplifying

5(7x + -3) = 230

Reorder the terms:

5(-3 + 7x) = 230

(-3 * 5 + 7x * 5) = 230

(-15 + 35x) = 230

Solving

-15 + 35x = 230

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 35x = 230 + 15

Combine like terms: -15 + 15 = 0

0 + 35x = 230 + 15

35x = 230 + 15

Combine like terms: 230 + 15 = 245

35x = 245

Divide each side by '35'.

x = 7

Simplifying

x = 7

5 0

4 years ago

babunello [35]

From the problem, you can get this equation:
Jane is 2 years older than Sally
J=z+2
David is 4 times older than Jane.
D=4J

Write two equivalent expressions that represent David’s age in terms of Sally’s age, z, and explain how the two expressions relate to one another.Sally is z years old.
From the 2 equation above, you can get:
D=4J
D=4(z+2)
D=4z+8

D-8=4z
(D-8)/4=z
The two equivalent expression would be D=4z+8 and (D-8)/4=z

The expression that more usefull would be D=4z+8 if you want to determine David age.

4 0

4 years ago