L2 Calculus

Question Bank

Gradients Tangents Increasing/Decreasing Stationary Points Antidifferentiation Sketching Optimisation Rates of Change Kinematics
Achieved

A function is given by $f(x) = 4x^4 - 5x^3 + 2x$. Find the gradient of the graph of the function at the point where $x=-1$.

Achieved

Find the gradient of the function $f(x) = \frac{1}{3}x^3 + 2x^2 - x + 10$ at the point where $x=3$.

Achieved

Find the gradient of the function $f(x) = (x + 3)^2$ at the point where $x = 2$.

Achieved

Find the gradient of the function $f(x) = (2x - 1)(x + 4)$ at the point where $x = -2$.

Achieved

Find the gradient of the function $f(x) = \frac{x^3 + 4x^2}{x}$ at the point $(3, 15)$.

Achieved

For the curve $y = 2x^2 + 3x - 7$, find the value of $x$ where the gradient is equal to $-4$.

Achieved

For the curve $y = x^3 - 3x^2 + 2x - 5$, find the value(s) of $x$ where the gradient is equal to 5.

Achieved

For the function $f(x) = x^3 - 6x^2 + 9x + 1$, find the value(s) of $x$ where the gradient is equal to 0.

Merit

The function $f(x) = 2x^2 - 5x + 3$ passes through the point where $y = 0$.

Find the gradient of the function at this point.