Show:
Tangent Line
Critical & Inflection Points
Chain Rule
Analyzing Functions
Normal Line
100
What is the tangent line of the equation y= x^3-3x^2+x at the point (2, -2)?
y=x-4
100
What are the critical points for the function f(x)=x^3+3x^2−45x?
x=3 and x=5
100
What is the derivative of f(x) = sin (2x^2)?
f'(x)= 4x⋅cos(2x^2)
100
What is the direction interval chart for the following function y= -(x^3)/3 +x^2
Increasing: (0,2) Decreasing: (-inf, 0), (2, inf)
100
What is the normal line of the equation f(x)= (x^2+3)^(1/2) at the point (-1,2)?
y=2x+ 4
200
What is the equation of the tangent line f(x)= x^3-3x^2+2 at x=3?
y=9x-25
200
What are the inflection points for the function y= -2x^3+3x^2
x= 0.5
200
What is the derivative of y = tan (5x^3)?
y'= 15x^2⋅sec^2 (5x^3)
200
What is the concavity interval chart for the following function y= -(x^3)/3 +x^2
Concave up: (-inf, 1) Concave down: (1, inf)
200
What is normal line of y= x^3-x^2-2 at x=1
y=-x-1
300
What is the equation of the line tangent to the equation y= - 5 / (x^2+1) at the point (-1, -5/2)?
y= - (5/2)x - 5
300
What are the critical points for f(x)= x^4-4x^3?
x= 0 and x=3
300
What is the derivative of f (x) = cos (−3x^2 + 2)^2
f'(x)= 12x(−3x^2 + 2)⋅sin(−3x^2 + 2)^2
300
What is the direction interval chart for the following function y= (7x^2 - 7) / x^3
Increasing: (-1.73, 0), (0, 1.73) Decreasing: (-inf, -1.73)(1.73, inf)
300
What is the normal line of y=(2x-8)^(1/3) at the point (0, -2)?
y=-6x-2
400
What is the line of tangency where x= 4, for the function y= (5x+5)^ 1/2?
y= 0.5x+3
400
What are the inflection points for f(x)= x^4-4x^3?
x=0 and x=2
400
What is the derivative of y =(2x^5 + 3)cos (x^2)?
y'= −2x( 2x^5+3)⋅sin(x^2)+10x^4⋅cos(x^2)
400
What is the direction interval chart for the following function y= (7x^2 - 7) / x^3
Concavity Up: (-2.45, 0), (2.45, inf) Concave Down: (-inf, -2.45), (0, 2.45)
400
What is the normal line of y= 2/ (x-3) at the point x=5?
y=2x-9
500
What is the equation for the line tangent to the equation y=-2tan(x) at the where x= -pi ?
y= -2x-2pi
500
What are the critical AND inflection points for f(x)= -x^4+3x^2-30?
critical points: x=0, x=-1.22, x=1.22 inflection points: x=-0.71 and x= 0.71
500
What is the derivative of y =(−2x^2−5) / cos (2x^3)?
(−4xcos (2x^3) + 6x^2⋅sin(2x^3)(−2x^2−5)) / cos^2 (2x^3)
500
What is the concavity interval chart for the following function y= x^3-3x
Concave Up: (-inf, -1), (0.5, inf) Concave Down: (-1, 0.5)
500
What is the normal line for the equation y= -sin(2x) at (x= pi/2)?
y= -0.5x- (pi/4)