The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0
f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.
Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.
Answer:
The required equation is 
.
Step-by-step explanation:
The equation of line cd is
Slope intercept form of a line is
Where, m is slope and b is y-intercept.
Slope of line cd is 3.
The product of slopes of two perpendicular lines is -1.
Therefore slope of perpendicular line is 
.
Point slope form of a line is
Slope of perpendicular line is and line passing through the point (3,1).
Therefore the required equation is .
Answer:
-16
Step-by-step explanation:
you just add all of them together
Answer:
(x+1)(x-1)(x+3)(x-3)
Step-by-step explanation:
x4-10x^2+9
Group expression so that the coefficients of the x^2 terms add up to +9.
= x^4 -9x^2 - x^2+9
match coefficients in both groups
= x^4 -9x^2 - (x^2-9)
factor each group
= x^2 (x^2-9) - 1(x^2-9)
now factor out the common factor (x^2-9)
= (x^2-1)(x^2-9)
Finally, factor each quadratic factor
= (x+1)(x-1)(x+3)(x-3)
The 3 in 350 is in the hundred place and in 403 the 3 is in the ones place
