F(x)=2x^3-2x+1 relativeminimum

Step-by-step explanation:

F(x) = 2x³ - 3x + 1.

d/dx [2x³ - 3x + 1] = 6x² - 3.

Firstly, we wish to find the stationary points of F(x).

When 6x² - 3 = 0, x = -0.707 or x = 0.707.

Now we use Second Derivative test:

d/dx [6x² - 3] = 12x.

Since 12(-0.707) < 0, x = -0.707 is a relative maximum point.

Since 12(0.707) > 0, x = 0.707 is a relative minimum point.

Hence x = 0.707. To find the exact point you can substitute the value of x back into the equation 2x³ - 3x +1.

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step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places