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#1 2015-04-22 09:23:14

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Differentiation

1. Differentiate s = 3t^2 - 4t - 2 wrt t.
2. y = 4x^2 - ax + 6. Given that the rate of change of y wrt x is 2 when x = 1, find the value of a.
3. Find the gradient on the curve y = 4x^3 - 10x + 1 at the point where x = -1.
4. The gradient on the curve y = ax^2 - 3x + 4 where x = -2 is 13. Find the value of a.
5. Find the coordinates of the points on the curve y = 3x^3 - 4x + 2 where the gradient is 0.


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#2 2015-04-22 10:29:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2015-04-22 14:09:13

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Differentiation

These are exercises. You should hide your answers.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2015-04-22 14:44:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation

Will do.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2015-04-23 05:29:04

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

Excellent, bobbym. All answers are correct.


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#6 2015-04-23 05:46:15

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

6) Find the values of z for which dP/dz = 0 where P = 4z^3 - 2z^2 - 8z + 5.
7) Show that there is only one point on the curve y = x^4 - 32x + 10 where the gradient is 0 and find its coordinates.
8) Given that u = 4t^3 + 3t^2 - 6t - 1, find the values of t for which du/dt = 12.
9) Given v = 4s^2 - 12s - 7, find dv/ds. For what value of s is dv/ds = 4?
10) Given that the curve y = ax^2 + b/x has a gradient of 5 at the point (1, 1), find the values of a and b. What is the gradient of the tangent to the curve at the point where x = 1/2?


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#7 2015-04-23 15:53:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2015-04-24 10:39:33

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

You are right bobbym. Both answers are correct.


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#9 2015-04-24 11:10:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation

Hi;

For 10, which do you mean

or


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2015-04-26 09:16:49

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

Hi;
Answers for 8, 9 are correct too.
For (10), I mean the first (former).
Cheers.


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#11 2015-04-26 12:09:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2015-04-28 07:43:51

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation


Only a friend tells you your face is dirty.

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#13 2015-04-29 06:00:13

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

Thanks bobbym. I'm connected through via mobile so have a few problems with hiding text.


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#14 2015-04-29 06:15:42

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 407

Re: Differentiation

11) The curve given by y = ax^3 + bx^2 + 3x + 2 passes through the point (1, 2) and the gradient at that point is 7. Find the values of a and b.
12) Given y = 2x^3 - 3x^2 -12x + 5, find the domain of x for which dy/dx is greater or equal to 0.
13) The function P is given by P = a/t + bt^2 and when t = 1, P = -1. The rate of change of P when t = 1/2 is -5. Find the values of a and b.
14) Given that R = mp^4 + np^2 + 3, find dR/dp. When p = 1,  dR/dp = 12 and when p = 1/4, dR/dp = -3/4. Find the values of m and n.


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#15 2015-04-29 17:06:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differentiation

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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