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Increasing and Decreasing Functions

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a month ago

Increasing and Decreasing Functions Class 12th

Let α ∈ R and A be a matrix of order 3 × 3 such that det(A) = −4 and A + I = [1 a 1; 2 1 0; a 1 2], where I is the identity matrix of order 3 × 3.
If det((a + 1)adj((a – 1)A)) is 2?3?, m, n ∈ {0,1,2, ., 20}, then m + n is equal to:
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New answer posted

a month ago

Increasing and Decreasing Functions Class 12th

If Σᵢ₌₁ⁿ(xᵢ-a)=n and Σᵢ₌₁ⁿ(xᵢ-a)²=na, (n,a>1) then the standard deviation of n observations x₁,x₂,.,xₙ is:
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alok kumar singh

Contributor-Level 10

S.D.=√ (Σ (x-a)²/n - (Σ (x-a)/n)²) = √ (a-1).

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New answer posted

a month ago

Increasing and Decreasing Functions Class 12th

Let f(x) = 3sin?x + 10sin³x + 6sin²x - 3, x ∈ [-π/6, π/2]. Then, f is
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Raj Pandey

Contributor-Level 9

f' (x) = 12sin³xcosx+30sin²xcosx+12sinxcosx = 3sin2x (2sin²x+5sinx+2) = 3sin2x (2sinx+1) (sinx+2).
In [-π/6, π/2], sinx+2>0. 2sinx+1>0 except at x=-π/6. sin2x>0 for x∈ (0, π/2), <0 for x (-/6,0).
So f' (x)<0 on (-/6,0) (decreasing) and f' (x)>0 on (0, π/2) (increasing).

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