Mathematics

Applications of Derivatives

Grade 12 · High School

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Question 1 of 20Easy
The slope of the tangent to $f (x) = x^{2}$ at $x = 1$ is ...
Question 2 of 20Easy
The derivative of $f (x) = x^{3} - 3 x$ is ...
Question 3 of 20Easy
The stationary point of $f (x) = x^{2} - 4 x$ occurs at $x = \dots$
Question 4 of 20Easy
The slope of the tangent to $y = x^{2} + 1$ at $x = 2$ is ...
Question 5 of 20Easy
A function has a stationary point when ...
Question 6 of 20Easy
The function $f (x) = x^{2}$ is always increasing on the interval ...
Question 7 of 20Medium
The minimum value of $f (x) = x^{2} - 6 x + 5$ is ...
Question 8 of 20Medium
The stationary points of $f (x) = x^{3} - 3 x$ are at $x = \dots$
Question 9 of 20Medium
The maximum value of $f (x) = - x^{2} + 4 x$ is ...
Question 10 of 20Medium
The function $f (x) = x^{2} - 2 x - 3$ is decreasing on the interval ...
Question 11 of 20Medium
The equation of the tangent to $y = x^{2}$ at $x = 1$ is ...
Question 12 of 20Medium
The function $f (x) = 2 x^{3} - 3 x^{2}$ has a local maximum at $x = \dots$
Question 13 of 20Medium
A particle's position is $s (t) = t^{2} + 3 t$ . Its velocity at $t = 2$ is ...
Question 14 of 20Medium
The values of $x$ satisfying the critical points of $f (x) = x^{3} - 12 x$ are ...
Question 15 of 20Hard
The local minimum value of $f (x) = x^{3} - 3 x^{2} + 4$ is ...
Question 16 of 20Hard
Two numbers add up to 20. The maximum product of the two numbers is ...
Question 17 of 20Hard
The minimum value of $f (x) = x^{4} - 4 x^{2}$ is ...
Question 18 of 20Hard
The tangent to $y = x^{3} - 3 x$ parallel to $y = 9 x - 1$ touches the curve at $x = \dots$
Question 19 of 20Hard
A particle's position is $s (t) = t^{3} - 6 t^{2}$ . Its acceleration at $t = 3$ is ...
Question 20 of 20Hard
An open box of volume $32 cm^{3}$ has a square base of side $x$ . For minimum surface area, the value of $x$ is ...

0/20 answered