For what values of \(x\) is the function \(f(x) = 2{x^3} - 3{x^2} - 12x\) increasing?

The stationary point on the curve \(y = {x^2} - 4x + 3\) is?

The curve \(y = a{x^2} + bx + 3\) has a stationary point at \(( - 1,2)\). The values of \(a\) and \(b\) are?

The second derivative of \(y = \dfrac{x}{{x - 1}}\) is?

The second derivative of \(x\sqrt x \) is?

The second derivative of \(\dfrac{1}{{\sqrt {1 + {x^2}} }}\) is?

For the curve \(y = {x^3} - 3x + 2\) the values of \(x\) for which the curve is concave up are?

For the curve \(y = {x^3} - 3{x^2} - 9x + 1\) the values of \(x\) for which the curve is concave down are?

\(y = a{x^3} - 3{x^2} - 12x + 2\) has a point of inflection at \(x = \dfrac{1}{2}\), the value of \(a\) is?

For what values of \(x\) is the function \(f(x) = {x^3} - 48x + 1\) is decreasing ?

A stationary point on the curve \(y = {x^4} - 32x + 48\) is ?

The adjacent diagram shows the sketch of \(y = {x^3} + 4{x^2} - 8\). The co-ordinates of the local maximum are?

The adjacent diagram shows the sketch of \(y = 3{x^4} + 4{x^3} - 12{x^2} - 24x\). The co ordinates of the local maximum are ?

The global maximum of the function \(y = {x^3} - 12x + 1\) in the domain \( - 4 \le x \le 4\) is ?

The global maximum of the function \(y = - {x^3} - 3{x^2} + 9x\) in the domain \( - 4 \le x \le 2\) is ?

The cost per hour of a bike ride is given by the formula \(C = {x^2} - 12x + 60\), where \(x\) is the distance traveled in km. The distance that gives the minimum cost is ? 

The surface area of a cylinder is given by \(S = 2\pi {r^2} + \dfrac{{500\pi }}{r}\) . The value of \(r\) that will give a minimum surface area is?

A 2\(m\) length of wire is cut into 2 pieces and each piece is bent to form a square. Given that the length of a piece is \(x m\), then the total area \(A\) of the two squares can be expressed as ?

Given that \(f'(x) = \,3{x^2} + 2x + 2\) and \(f(2)\)=1 then \(f(1)\)= ?

The gradient of the tangent to a curve is given by \(\dfrac{{dy}}{{dx}} = 4 - 6x\) and the curve passes through the point \((-1,1)\). The equation of the curve is?

Given that \(f''(x) = 3x\) , \(f'(0) = 3\) and \(f(-1)=2\) then \(f(2)=\)?

The adjacent diagram shows the sketch of \(y = - {x^3} - {x^2} + 4x\). The co-ordinates of the point of inflection are?

The global maximum of the function \(y = 3{(x + 1)^3}\) , where \( - 2 \le x \le 0\) is ?