Find equation of tangent..

**Klutz** · Sep 14th 2010, 03:58 AM

Find the equation of the tangent to the curve f (x) = 2x^2 - 4x + 4 which is perpendicular to the line y = -1/4x + 4.

I worked it out but got it slightly wrong and I dont know what I did incorrectly.
Could someone please clarify?

So what I did was I said okay. The gradient for the tangent is m=4.
and f'(x)=4x-4 so if the m=4, then x would equal 0.
If x=0, y=4 when you sub x=0 into f(x).

so i put it into the formula and got:
y-4=4(x-0)
y=4x+4

The answer is 4x-4.

Maybe its just a silly mistake that I can't point out and maybe its not. Anyone like to point it out?

**acevipa** · Sep 14th 2010, 04:09 AM

The gradient of the tangent is 4. So when $m=4, x=2$ .

$f'(x)=4x-4\Rightarrow 4=4x-4\Rightarrow x=2$

When $x=2, y=4$

Using the point-gradient form

$y-y_1=m(x-x_1)$

$y-4=4(x-2)$

$y=4x-4$

**Klutz** · Sep 14th 2010, 04:11 AM

Oh i get it now thanks!

**acevipa** · Sep 14th 2010, 04:17 AM

Since its perpendicular to the line, the product of the gradients of the lines equals -1

$m_{1}m_2=-1\Rightarrow -\frac{1}{4}m_T=-1\Rightarrow m_T=4$

So the gradient of the tangent is 4.

You know that $f'(x)=4x-4$ , which is the gradient function.

The gradient equals 4 when $f'(x)=4$

$4x-4=4\Rightarrow 4x=8\Rightarrow x=2$

**Klutz** · Sep 14th 2010, 04:20 AM

yeah. for some reason before your math equatoins didnt load on your last post thats why i was confused but thanks for the thorough explaination

**acevipa** · Sep 14th 2010, 04:24 AM

No worries. Have a good one

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