(2.01) solve -2(2x + 5) - 3 = -3(x - 1)

2 answers:

6 0

<span>solve -2(2x + 5) - 3 = -3(x - 1)

-4x - 10 -3 = -3x + 3
-4x - 13 = -3x + 3

Add 3x to both sides
-4x - 13 +3x = -3x +3

Simplify
-x - 13 = 3
Add 13 to both sides
-x - 13 + 13 = 3 + 13

Simplify
-x = 16

multiply both sides by (-1)
x = -16</span>

liq [111]3 years ago

3 0

-2(2x + 5) - 3 = -3(x - 1)...distribute thru the parenthesis
-4x - 10 - 3 = -3x + 3 ...simplify
-4x - 13 = -3x + 3...add 3x to both sides
-4x + 3x - 13 = 3 ...add 13 to both sides
-4x + 3x = 3 + 13 ...combine like terms
-x = 16 ... multiply by -1 to make x positive
x = -16

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Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} +750)) \:and \: (0, - 6) \: and\: ( \frac{ \sqrt{15} }{5} , \frac{1}{125} ( - 6 \sqrt{15} +750))$