OCR C1 Differentiation Question?

lola1993

Hey

I'm having problems with this question and would be grateful of some help!

Given that y=ax^2 + bx -a^2 has gradient -4 at (-2,-13), find possible values for a and b.

Thanks :smile:

Reply 1

spread_logic_not_hate

lola1993

Hey

I'm having problems with this question and would be grateful of some help!

Given that y=ax^2 + bx -a^2 has gradient -4 at (-2,-13), find possible values for a and b.

Thanks :smile:

You know that when x = -2, y = -13. You also know that

\dfrac{dy}{dx} = -4

when x = -2.

Can you go from there?

Reply 2

Wednesday Bass

So you find dy/dx

\displaystyle{\frac{dy}{dx}} = 2ax + b

And you know dy/dx = -4 at (-2, -13), sub those values in. So you end up with:

-4 = -4a + b \Rightarrow b = 4a - 4

Sub that into the original equation.

Reply 3

lola1993

So you find dy/dx
\displaystyle{\frac{dy}{dx}} = 2ax + b
And you know dy/dx = -4 at (-2, -13), sub those values in. So you end up with:
-4 = -4a + b \Rightarrow b = 4a - 4
Sub that into the original equation.

I tried differentiating to get the gradient but surely its 2ax + b - 2a ?

Reply 4

Wednesday Bass

lola1993

I tried differentiating to get the gradient but surely its 2ax + b - 2a ?

There's no (-2a), because you''re differentiating with respect to x. And since it's (-a^2) in the original equation. When you differentiate it, you treat it as you would any other number.