Derivation - practice problems

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 44

Derivation
Exists a function whose derivation is the same function?
Derivative 4239
Determine the value of the derivative of the function f (x) = 10
Derivative 4267
Calculate the value of the sixth derivative of this function: f (x) = 93x.
Derivative 4251
What is the value of the derivative of this function: f (x) = 12x
Continuity 4087
Specify the point at which the sgn x function has no continuity.
Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal.
Derivative 4041
Is there a continuous function that has no derivative at every point?
Parabola with abs
A). Sketch the graph of the function f(x)=x * absolute(x) = x * |x| b). For what values of x is f(x) differentiable c). Find F(x)
Derivative 4266
Calculate the value of the fifth derivative of this function: f (x) = 3x² + 2x + 4
Summands 4213
Divide the number 28 into two summands so that their product is maximal.
Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2
Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder.
Use L
Use L Hospital's rule to solve (i) Lim x²+5x-14/x²-5x+6 X—>2 (ii)Lim x³+x²-x-1/x²-2x-3 X—>3
Intersection of Q2 with line
The equation of a curve C is y=2x² - 8x +9, and the equation of a line L is x + y=3. (1) Find the x-coordinates of the points of intersection of L and C. (ii) show that one of these points is also the
The position
The displacement function S=t³-2t²-4t-8 gives the position of a body at any time t. Find its acceleration at each instant time when the velocity is zero.
Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
Dogde Caliber
The petrol kilometers M (unit: kilometers per liter) of Dogde Caliber car is modelled by the function M(s) = - 1/28s² + 3s- 31 What is the car best petrol kilometers and what speed is attained?

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