IB Maths SL, Tangent line

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

IB Maths SL, Tangent line

IB Mathematics SL – Derivatives, Differentiation, Equations of Tangent and Normals

How can we find the equation of the tangent to the curve $f(x)= x^2-5x$ that is parallel to the line with equation $y=3x+2$.

Thanks
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm

Re: IB Maths SL, Tangent line

IB Mathematics SL – Derivatives, Differentiation, Tangent and Normals

We know that the gradient of a curve $f(x)$ at any point $(x_{0},y_{0})$ is equal to the gradient of the tangent ($m_{T}$) to the curve at that point.

$f'(x)=2x-5$

and the gradient of the tangent must be equal to $3$ since is parallel to the line $y=3x+2$

$m_{T}= f'(x)=2x-5=3\Rightarrow 2x=8\Rightarrow x=4$

and the equation of the tangent is given by the following formula

$y-y_{0}=f'(x_{0})(x-x_{0})$

where in this case

$(x_{0},y_{0})=(4,-4)$

and finally the equation of the tangent is

$y-(-4)=3(x-4) \Rightarrow y=3x-16$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

Re: IB Maths SL, Tangent line

thanks miranda!!
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm