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

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.

Only a friend tells you your face is dirty.

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

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

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

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

Excellent, bobbym. All answers are correct.

Only a friend tells you your face is dirty.

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

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?

Only a friend tells you your face is dirty.

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

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

You are right bobbym. Both answers are correct.

Only a friend tells you your face is dirty.

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

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

Hi;

Answers for 8, 9 are correct too.

For (10), I mean the first (former).

Cheers.

Only a friend tells you your face is dirty.

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

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

Only a friend tells you your face is dirty.

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

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

Only a friend tells you your face is dirty.

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

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.

Only a friend tells you your face is dirty.

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

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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