Max & Min Values
Find the critical numbers of the function if possible: f(x)=x^3+6x^2-135x
x = 5, -9
Differentiate y = ln (x^2)
y' = (2x)/(x^2)
x=(3-ln(2))(1/4)
Find lim x->oo (e^x)/(x^2)
infinity
Differentiate f(x)=sin^-1 (x+1)
f'(x)=1/[1-(x+1)^2]^1/2
Find the absolute max and min values of f(x)=x^3-3x^2+1 where -1/2 <= x <= 4
Absolute max = 17 and absolute min = -3
Differentiate f(x)= 4 log3 (t) - ln t
f'(x)=4/(t ln (3)) - 1/t
Express the given quantity as a single logarithm: ln (a+b)+ln(a-b)-6 ln (c)
ln[(a^2-b^2)/c^6]
Find lim x->0 (sin (2x))/(tan (3x))
2/3
Differentiate f(x) = cos^-1(3x+x)
f'(x)=-(6x+1)/[1-(3x^2+x)^2]^1/2
Find the absolute maximum and minimum values of f(x)=7 cos (x) where -3pi/2 <= t <= 3pi/2
Absolute max = 7 and absolute min = -7
Differentiate f(x)=(1+5t)/ln (t)
f'(t)=[5 ln(t)-(1+5t)(1/t)]/(ln (t))^2
Find the inverse function of f(x)=x^3+5
f^-1(x)=(x-5)^(1/3)
Find lim x->0+ (x ln(x^4))
0
Differentiate y = x arctan(x^1/2)
y'=(x^1/2)/2(1+x) + arctan (x^1/2)
Find the critical numbers of the function if possible: f(x)=(x-2)/(x^2+1)
x = 2-(5)^1/2, 2+(5)^1/2
Differentiate f(x)=7x ln(3x) - 7x
f'(x)=7 ln(3x)
Evaluate sin^-1 (1/2)
pi/6
Find lim x->0 [tan (x) - x]/x^3
1/3
Differentiate y = arctan[(1+x)/(1-x)]^1/2
y' = 1/[2(1-x^2)^1/2]
Find the critical numbers of f(x)=6x^3+x^2+6x
DNE
Differentiate f(x)=ln (sinx+x^3)
f'(x) = [cos (x) + 3x^2]/[sin (x) +x^3]
Find the inverse of the function: f(x)=(2x-1)/(2x+5)
f^-1(x)=(5x+1)/(2-2x)
Find lim x->0 [x/(arctan (7x))]
1/7
Differentiate y = [arctan (6x)]^2
y' = [12 arctan (6x)]/(1+36x^2)