y=sin x+root3cos x find maximum and minimum value
Answers
EXPLANATION.
⇒ y = sin(x) + √3 cos(x).
As we know that,
Multiply and divide both numerator and denominator by 2, we get.
⇒ y = 2[sin(x) + √3 cos(x)]/2.
⇒ y = 2[sin(x)/2 + √3cos(x)/2].
As we know that,
Formula of :
⇒ sin(A ± B) = sin(A).cos(B) ± cos(A).sin(B).
Using this formula in equation, we get.
⇒ y = 2[sin(x).cos(60°) + cos(x).sin(60°)].
⇒ y = 2[sin(x + 60°)].
As we know that,
⇒ Range of sinθ = [-1,1].
⇒ y = [sin(x + 60°)] ∈ [-1,1].
⇒ y = 2[sin(x + 60°)] ∈ [-2, 2].
⇒ Maximum value = 2.
⇒ Minimum value = - 2.
MORE INFORMATION.
Note :
(1) = If f'(a) = 0, f''(a) = 0, f'''(a) ≠ 0 then x = a is not an extreme point for the function f(x).
(2) = If f'(a) = 0, f''(a) = 0, f'''(a) = 0 then the sign of f''''(a) will determine the maximum and minimum value of function that is, f(x) is maximum, if f''''(a) < 0 and minimum if f''''(a) > 0.
(3) = If f'(a) = f''(a) = f'''(a) = . . . . = f⁽ⁿ⁻¹⁾(a) = 0 and fⁿ(a) ≠ 0 if n is odd then f(x) has neither local maximum nor local minimum at x = a and this is point of inflection.
If n is even then fⁿ(a) < 0.
f(x) has a local maximum at x = a and if fⁿ(a) > 0 then f(x) has a local minimum at x = a.