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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: lacoste on June 11, 2009, 07:04:08 pm

Title: hellpppp!!!
Post by: lacoste on June 11, 2009, 07:04:08 pm: If f(x)= ax^2 + bx, solve for a and b given that the gradient at (3,5) = 1

thanks!!
Title: Re: hellpppp!!!
Post by: dcc on June 11, 2009, 08:18:52 pm: So we have the information given to us that $f(3) = 5$ and $f'(3) = 1$

Therefore:

$f(3) = 5 \implies 5 = 9a + 3b$

$f'(x) = 2ax + b$

$f'(3) = 1 \implies 1 = 6a + b$

Solving these simultaneously, we find that:

$f(x) = \frac{7}{3}x - \frac{2}{9} x^2$