L2 Calculus
Question Bank
The function $f(x) = kx^3 - 2x$ has a tangent with a gradient of 10 at the point where $x=-1$. Find the value of k.
The function $f(x) = 2x^2 - 8x + 5$ has a tangent line $y = 4x - 13$.
Use calculus to find the coordinates of the point where this tangent line touches the curve.
Find the equation of the tangent to the curve $y = x^2 + 3x$ at the point $(1, 4)$.
Find the equation of the tangent to the curve $f(x) = 2x^3 - 5x^2 + 4$ at the point $(1, 1)$ on the curve.
Find the equation of the tangent to the graph of $f(x) = x^2 - 6x + 11$ at the point where the gradient is 0.
Use calculus to show that the line $y = 4x - 3$ is a tangent to the graph of the function $f(x) = x^2 + 6x - 2$.
Use calculus to show that the line $y = 8x - 11$ is a tangent to the graph of the function $f(x) = x^3 - 4x + 5$.
Find the equation of the tangent to the curve $y = -x^2 + 4x + 1$ which has a gradient of 6.
Use calculus to find the value of $k$ if the line $y = 7x + k$ is a tangent to the graph of the function $f(x) = 2x^2 - 5x + 3$.
Use calculus to find the value of $k$ if the line $y = 4x + k$ is a tangent to the graph of the function $f(x) = -x^2 + 6x + 2$.
A cubic function $f(x) = x^3 + px^2 + qx + 7$ has the following properties:
• At $x = 1$, the tangent has gradient 5
• At $x = 2$, the tangent has gradient 8
Find the values of $p$ and $q$.
A tangent to the graph of the function $f(x) = -2x^2 + 8x - 3$ has a gradient of -4, and passes through the point $(a, -1)$, where $a$ is a constant. Find the value of $a$.
There are two points on the graph of the function $f(x) = x^3 - 6x^2 + 5x$ where the tangent to the graph passes through the origin $(0,0)$. Find the coordinates of these two points.
A tangent to the graph of the function $f(x) = \frac{1}{6}x^3 + kx + 3$ at a certain point P has gradient of 2.5 and intersects the graph again at $(6, 27)$.
Use calculus to find the coordinates of the point P.
The curve $y = x^3 - 9x^2 + 15x + 10$ has a tangent line at the point $(a, b)$ that also passes through the point $(1, 5)$, where $a \neq 1$.
Find the possible values of $a$.
The curve $y = x^3 + kx^2 - 8x + 5$ has a tangent line at the point where $x = 2$.
If this tangent line passes through the origin $(0, 0)$, find the value of the constant $k$.