Let f (x) = cos (x + 2 π / 3) + 2cos 2 x / 2, X belongs to R If f (b) = 1, B = 1, C = radical 3, find a

Let f (x) = cos (x + 2 π / 3) + 2cos 2 x / 2, X belongs to R If f (b) = 1, B = 1, C = radical 3, find a

F (b) = cos (B + 2 π / 3) + 2cos? B / 2 = 1 deduces cos (B + 2 π / 3) = - CoSb, so B + 2 π / 3 + B = π deduces B = π / 6
CoSb = (a? + C? - B?) / 2 * a * C = (a? + 3-1) / 2 * a * root 3 = root 3 / 2, push out a = 1 or 2~

The function f (x) = Xe ^ x + ax ^ 2 + 2x + 1 obtains the extremum (1) at x = - 1 to find the monotone interval of the function (2) If the function y = Xe ^ X has a unique intersection with the image of y = - x ^ 2-2x + m, find the value of M

(x) = xex ^ x + ax ^ 2 + 2x + 1F + 1F (x) = e ^ x + xex ^ x + 2aX + 2F + 2F (- 1) = 1 / E-1 / E-1 / e-2a + 2 = 2 (1-A) = 0, a = 11.f ~ (x) = e ^ x + Xe ^ x + 2x + 2 = (1 + x) (2 + e ^ x) when x > - 1, when x > - 1, 1 + x > 0, (1 + x) (2 + e ^ x) > 0, f (x) > 0, f (x) > 0, f (x) > 0, f (x) increases; when x < 1, when x < 1, when x < 1, f (x) increases; when x < 1, when x < 1, f (x) < 1, f (x) < 1 + x < 0, (1 + x) (2 + e ^ x) < 0, f '(x) < 0, f (...)

If f (x) = e to the - x power (cosx + SiNx), then f '(x) is equal to,

The answer is - E - x times 2 SiNx

When the value of independent variable x satisfies what condition, the value of function y = 3 / 2x-1 and y = 5x + 10 are equal? What is the corresponding function value

To meet the conditions, the following requirements are required:
(3/2)x－1＝5x＋10
==>3x－2＝10x＋20
==>－7x＝22
==>x＝－22/7
Therefore, when the value of the independent variable x is - 22 / 7, the function y = 3 / 2x - 1 and y = 5x + 10 have the same value
Put x = - 22 / 7 into y = 5x + 10
y=5×(－22/7)＋10=－40/7
That is, the corresponding function value is - 40 / 7

Find the range of y = 1 + SiNx + cosx + sinxcosx

Let t = SiNx + cosx=
2sin(x+π
4) Then t ∈[-
2，
2]．
From (SiNx + cosx) 2 = T2 {sinxcosx = t2-1
2．
∴y=1+t+t2-1
2=1
2（t+1）2．
∴ymax=1
2（
2+1）2=3+2
Two
2，ymin=0．
The value range is [0, 3 + 2
Two
2]．

The relationship between X + 1 power of y = 2 and x power of y = 2

The image of x power of y = 2 is shifted to the left by one unit, which is the image of X + 1 power of y = 2

The power of the function f (x) = (x 2 + X + 1) e belongs to r-monotone decreasing interval

If f '(x) = (x 2 + 3x + 2) e ^ x = (x + 1) (x + 2) e ^ x = 0 → x = - 1 or x = - 2, then the monotone decreasing interval is (- 2, - 1) and (- 1, + ∞)

The image of the power function f (x) = (m ^ 2-3m + 3) x ^ (m ^ 2-m-2) does not go through the origin and find the value of real number M. why should m ^ 2-3m + 3 be equal to 1?

The definition of solving power function f (x) = x ^ α
Let f (x) = (m ^ 2-3m + 3) x ^ (m ^ 2-m-2) be a power function
Then m ^ 2-3m + 3 = 1
The image of the power function f (x) = (m ^ 2-3m + 3) x ^ (m ^ 2-m-2) does not pass through the origin
Then m ^ 2-m-2 ≤ 0
M = 1 or M = 2 is obtained from ①
There are two things to know
M=1

How to get the absolute value symbol

If it is greater than or equal to 0, the absolute value is directly removed
If it is less than 0, the absolute value is removed and a negative sign is added before it

Draw the graph of the function y = | X-1 |

When x ≥ 1, y=x-1;
When x < 1, y = - x + 1
The list is as follows: