## IB Math Studies Tangent line

Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.

### IB Math Studies Tangent line

IB Mathematical Studies SL – Derivatives, Differentiation, Tangent Line

How can we find the equation of the tangent to the curve $f(x)=3x^2-5x$ that is parallel to the line with equation $y=3x+4$.

Thanks
hill

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Joined: Tue Mar 19, 2013 8:49 pm

### Re: IB Math Studies Tangent line

IB Mathematical Studies SL – Derivatives, Differentiation, Equation of Tangent

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.

$f'(x)=6x-5$

and the gradient of the tangent must be equal to $3$ since is parallel to the line $y=3x+4$

$m_{T}= f'(x)=6x-5=3\Rightarrow 6x=8\Rightarrow x=\frac{4}{3}$

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

$(x_{0},y_{0})=(\frac{4}{3},-\frac{4}{3})$

and finally the equation of the tangent is

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

Hope these help!!
elizabeth

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Joined: Mon Jan 28, 2013 8:09 pm

### Re: IB Math Studies Tangent line

Thanks Elisabeth!!
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm