Ten applications of the derivative, one each: implicit differentiation, related rates, tangent lines, critical points, the first derivative test…
10 questions • Zestly
• Given the relation $x^2 + xy + y^2 = 7$, what is the value of $\frac{dy}{dx}$ at the point $(1, 2)$?
• What is the equation of the tangent line to $f(x) = x^3 - 3x + 2$ at $x = 2$?
• Find all critical points of $f(x) = x^3 - 6x^2 + 9x$.
• For $f(x) = x^4 - 4x^3$, which list gives every $x$-coordinate at which the graph has a point of inflection?
• A rectangle has a perimeter of $20$ cm. What dimensions maximise its area?
• Which value of $c$ satisfies the Mean Value Theorem for $f(x) = x^2$ on $[0, 2]$?
• Using the linearisation of $f(x) = \sqrt{x}$ at $x = 4$, what is the approximation for $\sqrt{4.1}$, and how does it compare with the true…
• A particle moves along the $x$-axis with velocity $v(t) = t^2 - 4$, where $t$ runs over $-3 \le t \le 3$. On which set of times is the…
Want to check what you know — or test someone else?
Create your own quiz
See the full breakdown →
