# Find the coordinates of the point(s) at which the curve has the specified gradient

#### vizzy22

Hello.
I come here because I am in need of help. I am desperate. I just started learning at a university, and I do not understand a lot of things here. I will just add a picture of what I do not understand. If someone would help me, it'd mean the world to me... I do not understand how to do the D, and I am stuck in C also... so, firstly I need the D, but if you would be so kind and explain the C also, I'd be really grateful.
P.S. What would you suggest for a person who hasn't studied derivatives and slopes, but desperately needs to know this?

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#### skipjack

Forum Staff
If the given equation is effectively $y = x^n$, where $n$ is a constant, the gradient is given by the derivative of $y$, which is $nx^{n-1}\!$. To learn about this, read any textbook that introduces calculus for beginners or use an online course. If you can't cope with the former, try the latter (but it may take longer if it includes watching lengthy videos).

(d) Assuming that $x > 0$, you effectively have $y = x^{-3/2}\!$, so you need to solve $-{\small\dfrac32}x^{-5/2} = -\small\dfrac{3}{64}$, which simplifies to $x^{5/2} = 32$. That implies that $x^{1/2} = 2$, so $x = 4$.

If you do (c) similarly, you should find you need to solve $-2x^{-3} = 16$, which simplifies to $x^3 = -1/8$. Can you solve that?

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#### vizzy22

If the given equation is effectively $y = x^n$, where $n$ is a constant, the gradient is given by the derivative of $y$, which is $nx^{n-1}\!$. To learn about this, read any textbook that introduces calculus for beginners or use an online course. If you can't cope with the former, try the latter (but it may take longer if it includes watching lengthy videos).

(d) Assuming that $x > 0$, you effectively have $y = x^{-3/2}\!$, so you need to solve $-{\small\dfrac32}x^{-5/2} = -\small\dfrac{3}{64}$, which simplifies to $x^{5/2} = 32$. That implies that $x^{1/2} = 2$, so $x = 4$.

If you try to do (c) similarly, you should find you need to solve $-2x^{-3} = 16$, which simplifies to $x^3 = -1/8$. Can you solve that?
The thing is, how did you get $y = x^{-3/2}\!$ in D?
And in C, how do you get $x^3 = -1/8$ out of $-2x^{-3} = 16$, because for me it looks like $x^{-3} = -8$.

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#### vizzy22

Another thing - I was watching a video, and I had a question - why is the answer 1, not 1+1? Because I was wondering, if x' = 1, then where did that +1 go? Last edited by a moderator:

#### skipjack

Forum Staff
The function in (d) has denominator $xâˆšx$, which is $x*x^{1/2}$, i.e. $x^{3/2}$.
Note that $1/x^n = x^{-n}$. In (c), you get $x^{-3} = -8$, which is equivalent to $x^3 = -1/8$.

The derivative of 1 (or any constant) is zero, so f(x) and f(x) + c (where c is a constant) have the same derivative, provided that f(x) is differentiable.

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#### vizzy22

The function in (d) has denominator $xâˆšx$, which is $x*x^{1/2}$, i.e. $x^{3/2}$.
Note that $1/x^n = x^{-n}$. In (c), you get $x^{-3} = -8$, which is equivalent to $x^3 = -1/8$.

The derivative of 1 (or any constant) is zero, so f(x) and f(x) + c (where c is a constant) have the same derivative, provided that f(x) is differentiable.

Thank you, but on a different note. Do you think it is possible for me to catch up by studying on my own? In Latvia we weren't taught this in HS, yet in a university in Denmark, they are already expecting us to know this.

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#### skipjack

Forum Staff
It's possible, but could take quite a long time. During that time, you might fall behind on your university course, as it will be more difficult due to your lack of knowledge in various areas. Is the university course a mathematics course?

#### vizzy22

It's possible, but could take quite a long time. During that time, you might fall behind on your university course, as it will be more difficult due to your lack of knowledge in various areas. Is the university course a mathematics course?
European studies, international relations and business, so basically, I have take maths for the "'business" part.

#### skipjack

Forum Staff
That helps. Do you consider yourself to be someone who can readily learn from textbooks by yourself?

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#### vizzy22

That helps. Do you consider yourself to be someone who can readily learn from textbooks by yourself?
I am quite stressed about this, because I barely passed my math course in Latvia, and I don't consider myself to excel in this field. I am, however, a real hard worker, so I hope I can push myself to the limit of understanding.

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