Differentation

Question 1

If we have a profit function n(q) = mq+ c ,what is the gradient ?

Answer 1

the gradient is the change in profit/ change in production levels.

Question 2

When looking at a parabolae, how do we find gradient of the curve at a specific point?

Answer 2

We find the gradient of the tangent at that point

Question 3

What is a chord?

Answer 3

It is a line segement joining two points on a curve

Question 4

What can we use chords to do?

Answer 4

We can use chords to estimate the gradient

Question 5

Calculate the gradient

Answer 5

meaning the gradient at any point of the curve is 2x ( two times the value of x

x =2

m =4

Question 6

-So the gradient of the curve y = f(x) at the point (x,f(x)) is equal to what?

Answer 6

The gradient of the tangent to that point of the curve

Question 7

What is the differentation notation

Answer 7

this tells us to differentiate f(x) with respect to x

Question 8

if we have the curve y = x^2, what is the gradient at point (2,0)

Answer 8

Question 9

Whats the derative of square root x?

Answer 9

Question 10

Answer 10

Question 11

What is the constant mulitiple rule of differentation?

Answer 11

Question 12

Answer 12

Question 13

What is the sum rule of differentation?

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Not everything we can differentiate using these rules, such as what?

Answer 16

Division and multplication( this uses different rules)

Question 17

We are now going to look at finding the equation of the tangent to the curve?

The curve y = x^2 is the equation of the parabolae, the line of the point is (2,4) and we know the gradient is 4, calculate the equation of tangent?

Answer 17

Question 18

Answer 18

Question 19

What is the gradient of the tangent for the parabolae y = x^2 + x -3 (3,9)

and y = x^2+x-3 at point (2,3)

Answer 19

1) f’(x) = 2x + 1 = 2(3)+1 = 7
2) f’(x) = 2(2)+1 = 5

Question 20

Answer 20

Question 21

Answer 21

Question 22

find their gradients and hence find the equation of the tangent lines of these points.

Answer 22

Question 23

Find the equation of the line and their gradients

Answer 23

the equation is acc y = 3/4x+1