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C1 A differentiation question

Hello,

Would anyone know how to approach this question?

Given that f:x (ax+b)^3, x ℝ, and that when x = 2, f(x) = 1, and f'(x) = 6, find the values of a and b.

The answer at the back of my book says, a = 2 and b = -3.

I think I am supposed to use the chain rule. If so, how would I go about setting up the equation?

Thanks.
You need to setup simultaneous equations.

f(x) = 1 so (ax+b)^3 = 1 (this is your first equation)

f'(x) = 6 so (by using the chain rule) 3a(ax+b)^2 = 6 (this is your second equation)

What examboard are you doing maths with? With edexcel we didn't start using the chain rule until C3
Reply 2
Original post by RTL133
Hello,

Would anyone know how to approach this question?

Given that f:x (ax+b)^3, x ℝ, and that when x = 2, f(x) = 1, and f'(x) = 6, find the values of a and b.

The answer at the back of my book says, a = 2 and b = -3.

I think I am supposed to use the chain rule. If so, how would I go about setting up the equation?

Thanks.


x=2, y=1 gives an equation in a and b
x=2, dy/dx = 6 gives another equation in a and b
I assume you don't know the chain rule at c1. But is there any way to convert (ax+b)^3 into an expression that you *do* know how to differentiate? [Hint: What functions do you know how to differentiate at the C1 level? There aren't very many of them...]
Original post by RTL133
Hello,

Would anyone know how to approach this question?

Given that f:x (ax+b)^3, x ℝ, and that when x = 2, f(x) = 1, and f'(x) = 6, find the values of a and b.

The answer at the back of my book says, a = 2 and b = -3.

I think I am supposed to use the chain rule. If so, how would I go about setting up the equation?

Thanks.



This isn't C1! It's C3 lol. Anyway, yeah use the chain rule!
you should get 3{ (ax+b) }^{ 2 } multiplied by the differential of the inside of the bracket. Then sub the values in
Reply 5
Thanks so much.

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