Mathematics Tes...

Consider the following statements

1. The stationary points of a function are the points where the slope of the tangent on that point will be  0.

2. The points of inflection are the points where the function will have neither maximum nor minimum.

3. The tangent of the function becomes vertical at stationary points. 

4. All the above.

What is the minimum value of |x|?

What is the condition that f(x) = x³ + x² + kx has no local extremum?

A rectangle is given with a perimeter of 48 cm. If the rectangle encloses maximum area possible, then the area of the rectangle will be

If x² + y² = 1, find the maximum value of x² + 4xy - y².

The maximum value of \(\rm \left(\dfrac{1}{x}\right)^x\)

A 24 cm long wire is bent to form a triangle with one of the angles as 60°. What is the altitude of the triangle having the greatest possible area?

In (0, π/2), function \(f(x)=\frac{x}{1+x \tan x}\), have

Let f(x) = x - 6  and g(x) = x² - 2x + 3 where x is a positive integer. Find x at which g(f(x)) + f(g(x) is minimum?

The function \(f(x)=k \sin x+\frac{1}{3}\sin3x\) has maximum value at \(x=\frac{\pi}{3}\), what is the value of k?