11.04 Tangents and normals
Interactive practice questions
Consider the curve given by the function $f\left(x\right)=x^3+5x$f(x)=x3+5x.
Find the first derivative of the function, $f'\left(x\right)$f′(x).
Enter each line of working as an equation.
Which of the following notation represents the gradient of the function $f\left(x\right)$f(x) at the point $\left(2,18\right)$(2,18)?
$f\left(18\right)$f(18)
$f'\left(2\right)$f′(2)
$f'\left(18\right)$f′(18)
$f\left(2\right)$f(2)
Using the derivative found in part (a), determine the gradient of the tangent $f'\left(x\right)$f′(x), at the point $\left(2,18\right)$(2,18).
Enter each line of working as an equation where $f'\left(2\right)$f′(2) is the subject.
At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^2$y=x2 is given by $y=4x-4$y=4x−4.
At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^3$y=x3 is given by $y=12x-16$y=12x−16.
Consider the parabola $f\left(x\right)=x^2+3x-10$f(x)=x2+3x−10.