L2 Calculus
Question Bank
Find the antiderivative of $f(x) = 6x^2 - 4x + 5$.
The gradient function for a curve is $f'(x) = 3x^2 - 5$. The curve passes through the point $(2, 0)$. Find the equation of the function $f(x)$.
The gradient function for a curve is $\frac{dy}{dx} = 8x^3 - 3$. The curve passes through the point $(1, 4)$. Find the equation for y.
The derivative of a function is $\frac{dy}{dx} = 2x^3 - 3x^2 + 4x$. If the curve passes through the point $(2, 5)$, find the equation of the curve.
The graphs of a function $f(x)$ and its derivative $f'(x)$ are shown. Use information from the graphs to find the equation of the function $f(x)$.
A curve $y = f(x)$ passes through the point $(2, 10)$ and has a gradient function $\frac{dy}{dx} = 3x^2 + 4x - 1$. Find the co-ordinates of the point on the curve where $x = -1$.
The gradient function of a curve is $\frac{dy}{dx} = 4x^3 - 6x + 5$. The curve passes through the point $(1, -3)$. Find the value of $y$ on the curve when $x=2$.
The second derivative of a function is given by $f''(x) = 6x - 4$.
Given that the gradient of the function at $x = 2$ is 7, and the function passes through the point $(1, 5)$, find the equation of the original function $f(x)$.
The gradient function of a curve is given by $f'(x) = px + 5$. The curve passes through the points $(1, 4)$ and $(-2, -5)$. Find the equation of the curve.
The derivative of a function is given by $f'(x) = 6x^2 - 6x - 12$. The graph of the function has a local maximum at the point $(-1, 15)$. Use calculus to find the value of the local minimum of the function.
Use calculus to find the quadratic function $f(x)$ that has the following properties:
- a turning point when $x = 2$
- a gradient of -6 when $x = 1$
- a value of 10 when $x = 0$
The graphs of a function $f(x)$ and its derivative $f'(x)$ are shown. Use information from the graphs to find the equation of the function $f(x)$.
The graphs of a function $f(x)$ and its derivative $f'(x)$ are shown. Use calculus and information from the graphs to find the coordinates of the minimum point of the function $f(x)$.
The second derivative of a function is given by $f''(x) = 12x + 6$.
Given that the function passes through the points $(1, 8)$ and $(2, 20)$, find the equation of the original function $f(x)$.
The gradient of a function is given by $f'(x) = 3x^2 - 6x$. The graph of the original function, $f(x)$, passes through the point $(1, 5)$.
Find the equation of the tangent to the graph of $f(x)$ at the point where $x=3$.
The gradient of a function is given by $f'(x) = 2x - 4$. The graph of the original function, $f(x)$, passes through the point $(1, 2)$.
Find the equation of the tangent to the graph of $f(x)$ at the point where $x=3$.