Given the function f (x) = X4 + AX3 + 2x2 + B, where a, B ∈ R. if the function f (x) has an extreme value only at x = 0, then the value range of a is______ ．

Given the function f (x) = X4 + AX3 + 2x2 + B, where a, B ∈ R. if the function f (x) has an extreme value only at x = 0, then the value range of a is______ ．

F '(x) = 4x3 + 3ax2 + 4x = x (4x2 + 3ax + 4) to ensure that function f (x) has extreme value only at x = 0, the equation 4x2 + 3ax + 4 = 0 must have no real root or only one root is 0 (but obviously not, rounding off). The discriminant is: (3a) 2-64 ＜ 0, ｜ 9A2 ＜ 64} - 83 ＜ a ＜ 83} the value range of a is (− 83, 83), so the answer is: (− 83, 83)

Given that a is a real number, the function f (x) = AX2 + 2x − 3 − a + 4a. Find the minimum value of function y = f (x) in the interval [0,1]

It can be seen from a ≠ 0 that the quadratic function f (x) = AX2 + 2x − 3 − a + 4A = a (x2 + 2aX + 4a2) − 4A − 3 − a + 4A = a (x + 2a) 2 − 3 − a (3 points) so (1) when - 2A < 0, that is, a > 0, the function y = f (x) is a monotone increasing function in the interval [0, 1], so the minimum value of the function is f (0) = 4a-a-3 (5 points)

Given the function f (x) = e ^ 2x-ax (1), find the monotone interval (2) of F (x). If there is a real number x belonging to (- 1,1], let
The known function f (x) = e ^ 2x ax
(1) Finding monotone interval of F (x)
(2) If there is a real number x belonging to (- 1,1], such that f (x)

It will be available in ten minutes. Just a moment, please

The radius of the bottom of the cone is 1 and the length of the generatrix is 4. An ant starts from a point a on the circumference of the bottom of the cone
To climb a circle along the side of the cone to the midpoint B of bus PA, what is the shortest distance for an ant to crawl?

You unfold the cone, flatten it, and draw a straight line at the two points, which is the shortest

Fill in the correct answer number in brackets. The equation of n more poplar trees than willow trees is () a willow trees - n = poplar trees B poplar trees + n = willow trees C poplar trees = n + willow trees D poplar trees - willow trees = n

Hanying warm for you
C
(or click "satisfied" in the upper right corner of the client)
It's my motivation to move forward! Your adoption will also bring you wealth value
If you don't understand,
Until the completion of understand this problem!

Draw the largest circle in a square of 900 square cm. The circumference of the circle is () cm and the area is () square cm

The perimeter is 30 π (PS: 30 PAI)
The area is 225 π (PS: 225)

Letter formula of side area of oblique prism

Side area s = l × S 0, l is the length of side edge, S 0 is the area of straight section (the section perpendicular to side edge)

Do you know arc length and radius to find chord length?
Arc length 960, radius 75, chord length?

The arc length divided by the radius is the center angle of the arc pair. The chord length uses the middle perpendicular theorem. If a vertical line is drawn from the center of the circle to the chord, the chord will be divided equally. If you calculate by yourself, it should be no problem. Note that the center angle obtained is a radian unit, not an angle unit

Sum: SN: 2 * 3 + 6 * 3 ^ 2 + 10 * 3 ^ 3 + 14 * 3 ^ 4 +... + (4n-2) * 3 ^ n
Such as the title

3*Sn＝2*3^2+6*3^3+…… +（4n-6）*3^n+（4n-2）*3^n+1
Sn-3Sn＝2*3+4*（3^2+3^3+3^4+…… +3^n）-（4n-2）*3^n+1
-2Sn＝6+18*（3^n-1-1）-（4n-2）*3^n+1
Sn＝（2n-1）*3^n+1-9*3^n-1+6

Understanding of ancient poetry

Jingkou Guazhou a water, Zhongshan only separated by several mountains
When will the moon shine on me?
The first two sentences narrate the journey to the north. When he went to the capital, he just looked back at Jiangning, showing his complex psychology of not going to take up his post. The last two sentences express his heart with the scenery, which not only brings comfort to himself from the reform, but also brings the idea of retiring as soon as possible, The earth is green. Of course, it's the spring breeze blowing green. But isn't the lush green grass and seedlings the actual effect of the reform measures such as the Qingmiao method? But officialdom is full of dangers. Looking at the bright moon shining on the Guazhou ferry and Zhongshan Mountain, I sigh "when will the bright moon shine on me?"