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c1 - Differentiation help

1. find the equation of the tangent to the curve with equation
y= x^3-3x^2-2x-6
at the point where it crosses the y-axis

2. Given the function f(x)=x^3+5x^2-x-4 find
a) f' (-2) b) the values of a such that f'(a) =56

3. find the equation of the normal to y=x^4-4x^3 at the point
for which x= 0.5

I've done the whole of the exercise except for these three. Any help guys?

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Reply 1

TenOfThem

Original post by longsightdon

1. find the equation of the tangent to the curve with equation
y= x^3-3x^2-2x-6
at the point where it crosses the y-axis

It is hard to see why this one is causing a problem - what have you tried

Reply 2

TenOfThem

Original post by longsightdon

2. Given the function f(x)=x^3+5x^2-x-4 find
a) f' (-2) b) the values of a such that f'(a) =56

Have you found f ' (x)

Reply 3

TenOfThem

Original post by longsightdon

3. find the equation of the normal to y=x^4-4x^3 at the point
for which x= 0.5

Again - this seems very straightforward - what have you done so far

Reply 4

longsightdon

Original post by TenOfThem

It is hard to see why this one is causing a problem - what have you tried

i get this one now

Reply 5

longsightdon

Original post by TenOfThem

Have you found f ' (x)

no idea how to do that

Reply 6

longsightdon

Original post by TenOfThem

Again - this seems very straightforward - what have you done so far

nothing, i dont know how to do it

Reply 7

TenOfThem

Original post by longsightdon

i get this one now

Original post by longsightdon

no idea how to do that

I a struggling to see how you did (a) if you do not know how to differentiate

Reply 8

longsightdon

Original post by TenOfThem

I a struggling to see how you did (a) if you do not know how to differentiate

I wouldn't ask for help if I didn't know what to do... Please can you help?...

Reply 9

TLHroolz

Original post by longsightdon

F'(x) is the same as dy/dx
So, for questions 2, differentiate.
Then for part a) plug in x=-2 into the differentiated function

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Reply 10

longsightdon

Original post by TLHroolz

F'(x) is the same as dy/dx
So, for questions 2, differentiate.
Then for part a) plug in x=-2 into the differentiated function

Posted from TSR Mobile

ok thank you. What do i do for b)

Reply 11

Thinking_Aloud

Original post by longsightdon

ok thank you. What do i do for b)

For B, you know what dy/dx is from part a so you put that equal to 56 and rearrange the equation to find x (or 'a' as it says in the question).

Reply 12

TLHroolz

Original post by longsightdon

ok thank you. What do i do for b)

So, they've replaced f'(x) with f'(a) and told you that it equals 56, so put x=a and set the whole equation equal to 56 (probably a quadratic)

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Reply 13

longsightdon

Original post by Thinking_Aloud

For B, you know what dy/dx is from part a so you put that equal to 56 and rearrange the equation to find x (or 'a' as it says in the question).

Original post by TLHroolz

So, they've replaced f'(x) with f'(a) and told you that it equals 56, so put x=a and set the whole equation equal to 56 (probably a quadratic)

Posted from TSR Mobile

ok thanks guys

Reply 14

longsightdon

Original post by TLHroolz

So, they've replaced f'(x) with f'(a) and told you that it equals 56, so put x=a and set the whole equation equal to 56 (probably a quadratic)

Posted from TSR Mobile

dya think you could help me with no 3?

Reply 15

TLHroolz

Original post by longsightdon

dya think you could help me with no 3?

So, again, differentiate. Do you know how to work out the gradient of normals from the coordinate geometry chapter?

Posted from TSR Mobile

Reply 16

longsightdon

Original post by TLHroolz

So, again, differentiate. Do you know how to work out the gradient of normals from the coordinate geometry chapter?

Posted from TSR Mobile

im getting really confused w/ it

Reply 17

davros

Original post by longsightdon

dya think you could help me with no 3?

For Q3, do you know how the normal relates to the tangent? In particular, how do you get the gradient of the normal if you know the gradient of the tangent at a point?

Reply 18

longsightdon

Original post by davros

For Q3, do you know how the normal relates to the tangent? In particular, how do you get the gradient of the normal if you know the gradient of the tangent at a point?