Take this Quiz: A-Level Maths: Applications of Differentiation | Zestly

Question 1

For the function $f(x) = x^4 - 4x^3 + 10$, which of the following statements are true regarding its stationary points?

Accepted Answer

There is a local minimum at $x = 3$.

Question 2

Identify the points of inflection for the curve $y = x^4 - 6x^2 + 5$.

Accepted Answer

$x = \pm 1$

Question 3

A spherical balloon is being inflated such that its volume increases at a constant rate of $10 	ext{ cm}^3/	ext{s}$. How fast is the radius increasing when the radius is $5 	ext{ cm}$? (Volume $V = \frac{4}{3}\pi r^3$)

Accepted Answer

$\frac{1}{10\pi} 	ext{ cm/s}$

Question 4

Which of the following functions are concave down for all $x$?

Answer

$f(x) = x^2$

Answer

$f(x) = -e^x$

Answer

$f(x) = -x^4$

Answer

$f(x) = \ln(x)$

Question 5

A rectangular box with an open top is to be made from a $12 	ext{ cm}$ by $12 	ext{ cm}$ square sheet of metal by cutting equal squares of side $x$ from the corners. What is the expression for the volume $V$ in terms of $x$?

Answer

$V = x(12-x)^2$

Answer

$V = x(12-2x)(12-x)$

Answer

$V = x(12-2x)^2$

Answer

$V = 12x^2 - x^3$