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3 years ago

If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Mathematics

2 answers:

Hoochie [10]3 years ago

7 0

Answer:

Step-by-step explanation:

Our "best" case is when $f'(x) = 3$ everywhere - if it changes it means $f(x)$ will grow faster. But if $f'(x)$ is constant, it means $f(x)$ is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)

Natalka [10]3 years ago

6 0

Answer:

$f'( x ) = \frac{f(b) - f(a)}{b - a} \\ = \frac{f(6) -f(a)}{6 - 1} \\ 3\leqslant \frac{f(6) - 10}{5} \\ 15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25$

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Which is an exponential decay function f (x)=3/4 (7/4)x f (x)=2/3 (4/5)-x. F (x)=3/2 (8/7)-x f (x)=1/3 (9/2)x

dsp73

The given functions are
$1.\, f(x)= \frac{3}{4}( \frac{7}{4})^{x} \\ \\2.\,f(x)= \frac{2}{3}( \frac{4}{5} ) ^{-x}\\\\3.\, f(x)= \frac{3}{2} ( \frac{8}{7} )^{-x}\\\\4.\,f(x)= \frac{1}{3} ( \frac{9}{2} )^{x}$

Evaluate the functions.
1. Because 7/4 > 1 and the exponent is positive,
the function does not decay.
2.Because 4/5 < 1 and the exponent is negative,
the function does not decay.
3. Because 8/7 > 1 and the exponent is negative,
the function decays.
4. Because 9/2 > 1 and the exponent is positive,
the function does not decay.

A composite plot the functions verifies the answer.

Answer: $f(x)= \frac{3}{2} ( \frac{8}{7} )^{-x}$

7 0

4 years ago

Read 2 more answers

The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plumm

lbvjy [14]

<h2>Answer:</h2>

<em><u>Percent value of A with respect to Percent value of B is,</u></em>

$30\%$

<h2>Step-by-step explanation:</h2>

In the question,

Let us say the value of the Baseball card A and B initially is = 100x

So, for Baseball card A in first 5 years percent increase = 20%

So,

Value after 5 years = 100x + 20% of 100x = 120x

<u>After 5 more years,</u>

Percent decrease = 50%

So,

<u>Value at the end of 10 years = 120x - 50% of 120x = 60x</u>

Now,

For Baseball card B, Percent increase in 10 years = 100%

So,

<u>Value of card B = 100x + 100% of 100x = 200x</u>

So,

<em><u>Percent value of A with respect to Percent value of B is,</u></em>

$\frac{60x}{200x}\times 100=30\%$

7 0

3 years ago

Can someone help with explanation please:)

il63 [147K]

Answer:

Step-by-step explanation:

Volume of triangular prism:

$V_{1}$ = $A_{base}$ × H

Volume of triangular pyramid:

$V_{2}$ = $\frac{A_{base} *H}{3}$

The total volume of figure is

V = $V_{1}$ + $V_{2}$

5 0

2 years ago

Write an algebraic expression for the word phrase c divided by 7.

Y_Kistochka [10]

Answer:

D. c/7

Step-by-step explanation:

An algebraic expression refers to the equation. In the question, it says to divide a number (c) by seven, giving you c/7

5 0

3 years ago

4. Which ordered pair is a solution of 3y + 2 = 2x - 5?

Lyrx [107]

Answer:

we determine that none of the ordered pair is a solution of $3y\:+\:2\:=\:2x\:-\:5$ as none of the ordered pairs satisfy the equation.

Step-by-step explanation:

Considering the equation

$3y\:+\:2\:=\:2x\:-\:5$

Putting (-5,2) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(2\right)\:+\:2\:=\:2\left(-5\right)\:-\:5$

$8=-15$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (0,-5) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(-5\right)\:+\:2\:=\:2\left(0\right)\:-\:5$

$-13=-5$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (5,1) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(1\right)+\:2\:=\:2\left(5\right)-\:5$

$5\:=-5$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (7,5) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(5\right)+\:2\:=\:2\left(7\right)-\:5\:\:$

$17=9$ ∵ L.H.S ≠ R.H.S

FALSE

From the above calculations, we determine that none of the ordered pair is a solution of $3y\:+\:2\:=\:2x\:-\:5$ as none of the ordered pairs satisfy the equation.

4 0

3 years ago