Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The gradient of the curve $=\frac{a}{x}+bx^2$ at the point (3,6) is 7. Calculate the values of a and b.

I did it,
$6=\frac{a}{3}+b(3^2) \tag{1} $ We also have: (derivative) $y'=-\frac{a}{x^2}+2bx \tag{2}$
$7=-\frac{a}{3^2}+2b(3) \tag{3} $
but it doesn't seen right.

the answer is a=-9, b=1

Can you help me out? thanks.

share|cite|improve this question
In equation $(1)$ a $b$ is missing. – user21436 Apr 13 '12 at 1:34
Your values of $a$ and $b$ are right. – user21436 Apr 13 '12 at 1:36
Why do you think you could be wrong? Anything particular you're doubtful about? – user21436 Apr 13 '12 at 1:38
yes, i don't know how to do further. thx :) – Sb Sangpi Apr 13 '12 at 1:42
It was not clear if you wanted us to check the answer or how to get that answer? Oh, well, there are answers now. – user21436 Apr 13 '12 at 1:44
up vote 1 down vote accepted

From $6=\frac a3+9b$ it follows that $a=18-27b$. Substituting into (3) we get $7=-\frac{18-27b}{9}+6b=3b-2+6b$, hence $b=1$ and $a=18-27=-9$.

share|cite|improve this answer
At the time of this comment, your reputation is $3935$, and mine is $3539$... interesting! – The Chaz 2.0 Apr 13 '12 at 1:43
@TheChaz A bit strange indeed. – azarel Apr 13 '12 at 1:47
how did $a=18-27b$, i got only $18=a+27b$, thx. – Sb Sangpi Apr 13 '12 at 1:58
Sb, if you don't know how to go from $$18 = a + 27b$$ to $$a = 18 -27b$$, then we might have a problem! – The Chaz 2.0 Apr 13 '12 at 2:01
aww..i see, so sorry, $a+27b=18$ then $a=18-27b$ – Sb Sangpi Apr 13 '12 at 2:05

If you multiply equation (3) by three, then add it to equation (1), you'll get $$27 = 27b$$

From this, the value of $a$ follows.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.